Get Ready BLM 4... Scatter Plots. The scatter plot shows the height of a maple tree over a period of 7 years. a) Identify the independent variable and the dependent variable. Describe the relationship between the variables. Predict the height of the tree after 0 years. Translations and Reflections. a) Translate the square units up and units to the right. Reflect the triangle in the line of reflection and then translate it units to the right.. a) Plot the rectangle with vertices (, ), (, ), (, ), and (, ) on a coordinate grid. On the same grid, plot the image of the rectangle after a reflection in the y-axis. On the same grid, plot the image of your rectangle in part after a translation of units left and unit up. Operations With Powers 4. Use the exponent laws to write each as a single power. a) 4 6 ( ) 5 ( 5) d) ( 4) 4 ( 4) e) ( ) 4 f) 5 6 (5 ) 4 g) ( ) ( ) h) ( ) 4 ( ) 5. Use the exponent laws to write each as a single power. a) 4 ( 7) ( 7) ( 7) ( ) 5 ( 4 ) 8 4 d) ( ) ( ) 4 4 ( 4) 5 0. 0. e) 0. 4 [( 0.4) ] f) ( 0.4) ( 0.4) Principles of Mathematics 0: Teacher s Resource BLM 4 Get Ready Copyright 007 McGraw-Hill Ryerson Limited
Section 4. Practice Master BLM 4.... Which scatter plot(s) could be modelled using a curve instead of a line of best fit? Explain. a). State whether each line of best fit is a good model for the data. Justify your answer. a). Are the relations in question linear or non-linear? Explain. 4. a) Complete the table of values for the relation between the area of a circle and its diameter. Then, make a scatter plot of the data. Diameter (cm) A = πr (cm ) 4 5 6 Describe the relation. Draw a curve of best fit for the data. d) Use your model to predict the area for a diameter of.5 cm. e) Use your model to predict the area for a diameter of 8 cm. 5. a) Complete the table for the surface area of a cube. Side Length, s (cm) 4 5 6 7 8 Surface Area, SA = 6s (cm ) Make a scatter plot of the data. Describe the relation. d) Draw a curve of best fit for the data. e) Use your model to predict the surface area for a side length of 7.5 cm. f) Explain why the graph is non-linear. Principles of Mathematics 0: Teacher s Resource BLM 4 Section 4. Practice Master Copyright 007 McGraw-Hill Ryerson Limited
Finite Differences Tables BLM 4 4... Principles of Mathematics 0: Teacher s Resource BLM 4 4 Finite Differences Tables Copyright 007 McGraw-Hill Ryerson Limited
Section 4. Practice Master BLM 4 6.... The table gives the approximate height of a cannonball for a 6-s flight. Time, t (s) Height, h (m) 0 0 5 40 45 4 40 5 5 6 0 a) Sketch a graph of the quadratic relation. Describe the flight path of the cannonball. Identify the axis of symmetry and the vertex. d) What is the maximum height that the cannonball reached? e) Verify that h = 5t + 0t can be used to model the flight path of the cannonball.. Use finite differences to determine whether each relation is linear, quadratic, or neither. a) x y x y 0 4 5 6 0 9 0 0 0 4 5 4 40 x y d) x y 5 5 9 7 5 5 7 49 9 8 7. A girl is skipping rope when a picture is taken of her. At the instant the picture is taken, her hands are m apart and the centre of the rope is directly above her head, m above her hands. a) Use this information to graph the relation modelling the shape of the rope. The positions of her hands are the x-intercepts, and the centre of the rope is the y-intercept. Describe the shape of the arch that the rope makes. 4. A ball is thrown upward with an initial velocity of 0 m/s. Its approximate height, h, in metres, above the ground after t seconds is given by the relation h = 5t + 0t + 5. a) Sketch a graph of the quadratic relation. Describe the flight path of the ball. Find the maximum height of the ball. d) How long does it take the ball to reach this maximum height? 5. The table shows the height of a ball as it moves, where x represents the distance along the ground and h represents the height above the ground, in metres. Distance (m) Height (m) 0 4 4 4 8 5 a) Sketch a graph of the quadratic relation. Describe the flight path of the ball. Identify the axis of symmetry, and explain why it is the axis of symmetry. d) Identify the vertex. e) What is the maximum height of the ball? f) Verify that h = x + x + can be used to model the flight path of the ball. Principles of Mathematics 0: Teacher s Resource BLM 4 6 Section 4. Practice Master Copyright 007 McGraw-Hill Ryerson Limited
Section 4. Practice Master BLM 4 8.... For each part, sketch the graph of all four quadratic relations on the same set of axes. a) y = x y =x y = x y = x y = (x + 4) y = (x ) y = (x + 8) y = (x 7) y = x y = x + y = x 0.5 y = x + 0.5. For each relation, i) sketch a graph of the parabola ii) label three points on the parabola iii) describe the transformations from the graph of y = x a) y = x y = x + 6. Write an equation for the quadratic relation that results from each transformation. a) The graph of y = x is translated 5 units upward. The graph of y = x is translated 9 units downward. The graph of y = x is translated 6 units to the right. d) The graph of y = x is translated 0 units to the left. 4. Write an equation for the quadratic relation that results from each transformation. a) The graph of y = x is reflected in the x-axis. The graph of y = x is reflected in the y-axis. The graph of y = x is compressed vertically by a factor of. d) The graph of y = x is stretched vertically by a factor of 6. 5. The relation h =.5x +.5 can be used to model a grasshopper s jump. h represents the height and x represents the horizontal distance travelled, where x, with all measurements in centimetres. a) Graph the relation. Determine the maximum height of the jump. Write a second equation to model the jump of a second grasshopper if it reaches a maximum height of.0 cm. Assume that the second grasshopper starts and lands at the same positions as the first. 6. The height, h, in metres, t seconds after a flare is launched from a boat can be modelled by the relation h = 5.5(t 4) + 86. a) What was the maximum height of the flare? What was its height when it was fired? How long after it was fired did the flare hit the water, to the nearest second? 7. A parabola y = ax + k passes through the points (, 5) and (, 9). Find the values of a and k. Principles of Mathematics 0: Teacher s Resource BLM 4 8 Section 4. Practice Master Copyright 007 McGraw-Hill Ryerson Limited
Section 4.4 Practice Master BLM 4 9.... Copy and complete the table for each parabola. Replace the heading for the second column with the equation for the parabola. a) y = (x ) + y = ( x + ) 4 y = (x + 4) + Property vertex axis of symmetry stretch or compression direction of opening values that x may take values that y may take y = a(x h) + k. Sketch each parabola in question.. Write an equation for the parabola that satisfies each set of conditions. a) vertex (, 4), opening downward with a vertical stretch by a factor of vertex (, ), opening upward with a vertical compression by a factor of vertex (, 4), opening downward with no vertical stretch 4. Write an equation for each parabola. a) 5. Find an equation for the parabola with vertex (, ) that passes through the point (, ). 6. A rocket travels according to the equation h = 4.9(t 6) + 8, where h is the height, in metres, above the ground and t is the time, in seconds. a) Sketch a graph of the rocket s motion. Find the maximum height of the rocket. How long does it take the rocket to reach its maximum height? d) How high was the rocket above the ground when it was fired? Principles of Mathematics 0: Teacher s Resource BLM 4 9 Section 4.4 Practice Master Copyright 007 McGraw-Hill Ryerson Limited
Section 4.5 Practice Master BLM 4.... Sketch each parabola. Label the vertex and the x-intercepts. a) y = (x + )(x 4) y = (x 6)(x + 4) y = (x + 8)(x + ) d) y = ( x )( x 7). Determine an equation in the form y = a(x r)(x s) to represent each parabola by considering the vertex and the x-intercepts. a). Consider the quadratic relation y = (x ). a) Sketch the parabola. Write the coordinates of the vertex. How many x-intercepts does the parabola have? 4. The path of a rocket is given by the relation h = 5(x )(x ), where x represents the horizontal distance, in metres, the rocket travels and h represents the height, in metres, above the ground of the rocket at this horizontal distance. a) Sketch the path of the rocket. What is the maximum height of the rocket? What is the horizontal distance when this occurs? d) What is the height of the rocket at a horizontal distance of 5 m? e) Find another horizontal distance where the height is the same as in part d). 5. The path of a kicked football can be modelled by the relation h = 0.0x(x 45), where h represents the height, in metres, above the ground and x represents the horizontal distance, in metres, measured from the kicker. a) When the ball hits the ground, how far has it travelled? If the goal post is 40 m away, will the kick clear the -m-high crossbar for a field goal? Principles of Mathematics 0: Teacher s Resource BLM 4 Section 4.5 Practice Master Copyright 007 McGraw-Hill Ryerson Limited
Section 4.6 Practice Master BLM 4.... Rewrite each power with a positive exponent. a) 4 d) ( 4) e) f) ( 4). Evaluate. a) 4 0 0 4 d) ( ) e) 8 f) 7 0 g) ( ) 7 h) ( ). Evaluate. a) 4 + 0 ( + ) 0 d) 9 + 9 + 9 0 4. Determine the value of x that makes each statement true. 4 a) x x = 6 ( ) = 8 ( ) x = 64 4 7 d) x 5 = 5 5. The half-life of radon- is 4 days. Determine the remaining mass of 00 mg of radon- after a) 8 days days 0 days 6. A culture of bacteria in a biology lab contains 000 bacteria cells. The number of cells in the culture doubles every day. This can be expressed by the equation N = 000 t, where N represents the number of bacteria cells and t represents the time, in days. a) Find the number of cells in the culture after days and after week. How many cells were in the culture days ago? Hint: days ago means t =. What does t = 0 indicate? 7. The number, N, of radium atoms remaining in a sample that started at 400 atoms can be represented by the equation N = 400 600, where t is the time, in years. a) What is the half-life of radium? How many atoms are left after 00 years? What does t = 0 represent? d) What do negative values of t represent? t 8. The half-life of beryllium- is.8 s. Determine the remaining mass of 00 g of beryllium- after a) 7.6 s 4.4 s 55.4 s Principles of Mathematics 0: Teacher s Resource BLM 4 Section 4.6 Practice Master Copyright 007 McGraw-Hill Ryerson Limited
Chapter 4 Review BLM 4 4... (page ) 4. Investigate Non-Linear Relations. Identify whether each scatter plot can be modelled using a line of best fit or a curve of best fit. a). Use the data in the table to answer the questions below. Value of the Time (years) Investment ($) 0 00 05 08 4 4 5 5 6 50 7 7 8 95 9 5 a) Make a scatter plot of the data and draw a curve of best fit. Describe the relation between value and time. Use your curve of best fit to estimate the value of the investment after 0 years. 4. Quadratic Relations. Use finite differences to determine whether each relation is linear, quadratic, or neither. a) x y 0 9 4 66 5 7 x y 0 0 x y 5 5 7 9 9 7 4. Susan throws a rock off a cliff that is 0 m tall. The height, h, in metres, of the rock above the ground can be related to the time, t, in seconds by the equation h = 5t + 0t + 0. a) Graph the relation. What is the maximum height of the rock? When does the rock reach its maximum height? Principles of Mathematics 0: Teacher s Resource BLM 4 4 Chapter 4 Review Copyright 007 McGraw-Hill Ryerson Limited
4. Investigate Transformations of Quadratics and 4.4 Graph y = a(x h) + k 5. Sketch the graph of each parabola and describe its transformations from the relation y = x. a) y = (x + ) y = x + y = x d) y = x 6. Copy and complete the table for each parabola. Replace the heading for the second column with the equation for the parabola. a) y = (x + ) + y = 4(x 5) y = ( x + ) d) y = (x ) 4 Property vertex axis of symmetry stretch or compression direction of opening values that x may take values that y may take y = a(x h) + k 7. Sketch each parabola in question 6. 8. A store can increase revenue by increasing the price of its T-shirts. The revenue, R, in dollars, can be modelled by the relation R = 50(d.5) + 4000, where d represents the dollar increase in price. a) Graph the relation for 0 d 0. What is the maximum revenue? What dollar increase corresponds to the maximum revenue? BLM 4 4... (page ) 4.5 Quadratic Relations of the Form y = a(x r)(x s) 9. Sketch a graph for each quadratic relation. Label the vertex and the x-intercepts. a) y = (x )(x + 6) y = ( x+ 8)( x ) y = x(x + 0) 0. The path of a jet plane in training manoeuvres is given by the relation h = 5(t + 0)(t 00), where h represents the height, in metres, above the ground and t is time, in seconds. a) Sketch a graph for this relation. At what time does the plane reach its maximum height? What is the maximum height? 4.6 Negative and Zero Exponents. Evaluate. a) 6 8 ( ) 0 ( ) 4 d) e) ( ) f) ( ) 5 g) 7 0 h) ( ). Evaluate. a) 6 6 (4 + 5) 0 4 + 4. Solve for x. a) x = 7 ( ) x = 5 5 4 x = 7 64 4. The half-life of sodium-4 is 6 h. a) What fraction of a sample of sodium-4 will remain after h? What fraction of a sample of sodium-4 will remain after 4 days? Write the fractions in parts a) and with a negative exponent with a base of. Principles of Mathematics 0: Teacher s Resource BLM 4 4 Chapter 4 Review Copyright 007 McGraw-Hill Ryerson Limited
Chapter 4 Practice Test BLM 4 6... (page ). The equation of the axis of symmetry for the parabola defined by y = (x 6) + is A x = 6 B y = C x = 6 D y =. The x-intercepts of the parabola y = 5(x 6)(x + 4) are A 4 and 6 B 5 and 6 C 5, 6, and 4 D 6 and 4. 5 0 is equal to A 5 B 5 C D 4. An equation for the parabola y = x after it is reflected in the x-axis and translated units to the right and 4 units down is A y = (x ) + 4 B y = (x ) 4 C y = (x ) 4 D y = (x + ) + 4 5. The fraction of the surface area of a pond covered by algae cells doubles every week. Today the pond surface is fully covered with algae. When was the pond half-covered? A yesterday B week ago C month ago D it depends on the size of the pond 6. Evaluate. a) ( ) + + 4 + d) ( 4 ) 0 7. The table shows the growth pattern for Michael, measured every months for the past years since his 8th birthday. Month Height (cm) 0 5 8 6 9 9 4 4 5 45 8 46 48 4 5 a) Plot the points on a grid and draw a line or curve of best fit. What type of relation does this line or curve of best fit represent? Use the graph to determine Michael s height in another year from the end of the data. d) What assumption do you need to make to answer part? 8. For the parabola y = ( x ), state a) the equation of the axis of symmetry the stretch or compression factor relative to y = x the direction of opening d) the values x may take e) the values y may take 9. Sketch an example of a linear relation, a quadratic relation, and a relation that is neither linear nor quadratic. Label each graph. Principles of Mathematics 0: Teacher s Resource BLM 4 6 Chapter 4 Practice Test Copyright 007 McGraw-Hill Ryerson Limited
0. Use finite differences to determine whether each relationship is linear, quadratic, or neither. a) x y 8 5 4 5 4 x y 5 0 9 9. A flying bird drops a seed. The height, h, in metres, of the seed above the ground can be modelled by the relation h = 5t + 5, where t is in seconds. a) Sketch the relation. How far above the ground is the bird when it drops the seed? How long does the seed take to hit the ground?. The path of a flying disc can be modelled by the relation h = 0.065d(d ), where h is the height, in metres, above the ground, and d is the horizontal distance, in metres. a) Sketch a graph of the relation. At what horizontal distance does the disc land on the ground? At what horizontal distance does the disc reach its maximum height? d) What is the maximum height? BLM 4 6... (page ). Richard plans to divide his money among his six children when he dies, according to the following formula: The oldest child will get of the estate, the second-oldest child will get of what is left, the third child will get of what is left after the first two children get their inheritance, and so on down the line. a) What fraction of the estate will each child get? If Richard dies with a net worth of $6.4 million, how much will each child get? Will there be any money left over once the estate is settled? If so, how much remains? 4. To increase revenue, a sports store has decided to increase the cost of a baseball glove. They expect that for every $5 increase in price from the current price of $40, three fewer gloves will be sold per week than the current 60 per week. The revenue relation is R = (60 x)(40 + 5x), where R represents the revenue, in dollars, and x represents the number of price increases. a) Graph the relation and label the x-intercepts. Determine the maximum revenue per week for the store. How many times was the price increased for this maximum revenue? d) What is the price of a glove when revenue is at its maximum? e) How many gloves were sold per week to generate this maximum revenue? Principles of Mathematics 0: Teacher s Resource BLM 4 6 Chapter 4 Practice Test Copyright 007 McGraw-Hill Ryerson Limited
Chapter 4 Test BLM 4 7... (page ). Sketch a graph for each parabola. Label the coordinates of the vertex and the equation of the axis of symmetry. a) y = x 4 y = (x ) + y = ( x+ 5) 4. Sketch a graph for each relation. Label the x-intercepts and the vertex. a) y = 5(x 5)(x + ) y = (x + )(x 4). Evaluate a) 0 + ( ) ( 0 4 0 + ( ) ) 0 d) ( 0 4 0 + ( ) ) 4. Determine an equation to represent each parabola. a) 5. Use finite differences to determine whether each relationship is linear, quadratic, or neither. a) x y 5 7 4 7 x y 0 0 8 7 x y 6 4 6 40 8 47 0 54 Principles of Mathematics 0: Teacher s Resource BLM 4 7 Chapter 4 Test Copyright 007 McGraw-Hill Ryerson Limited
6. The table shows the growth pattern of a circular oil spill in calm water as oil spills out of the ruptured tank of a tanker. The spill began at time t = 0. Time, t (h) Radius, r (m) Area, A (m ) 0. 6.6. 0. 4.0 50. 4.7 69.4 4 5.5 95.0 5 6. 6 7. 7 7.8 8 8.9 a) Complete the Area column using the formula A = πr. Round your answers to the nearest tenth. Make a scatter plot of the data in the first two columns. Draw a line or curve of best fit. Make a scatter plot of the data in the first and third columns. Draw a line or curve of best fit. d) Use your graph in part to determine the radius of the oil spill after 0 h. Then, use the formula A = πr to find the area at this time. e) Use your graph in part to determine the area after 0 h. Then, compare this area with the area you calculated in part d). BLM 4 7... (page ) 8. A parabola y = ax + k passes through the points (, ) and (, ). Find the values of a and k. 9. The half-life a radioactive material is weeks. Determine the mass of 500 mg of the material that is still radioactive after a) 6 weeks weeks 8 weeks 0. The path of a ball as it travels through the air after being fired out of a cannon can be modelled by the equation h = 0.05d(d 0), where h is the height, in metres, above the ground and d is the horizontal distance, in metres. a) Sketch a graph of the relation. At what horizontal distance does the ball land? At what horizontal distance does the ball reach its maximum height? d) What is the maximum height? 7. Lucy throws a stone from the top of a cliff into the water below. The height h, in metres, of the stone after t seconds is given by the relation h = 4.9t + 5t + 00. a) Sketch a graph of the quadratic relation. Describe the flight path of the stone. Find the maximum height of the stone. d) How long does it take the stone to reach this maximum height? Principles of Mathematics 0: Teacher s Resource BLM 4 7 Chapter 4 Test Copyright 007 McGraw-Hill Ryerson Limited
BLM Answers BLM 4 9... (page ) Get Ready. a) independent: time in years, dependent: height in centimetres linear relationship 56 cm. a) Section 4. Practice Master. The data in part could be modelled using a curve of best fit, because the data follow a curve, not a straight line.. a) Yes, all data points are evenly spread around the line. No, this should be a curve of best fit, as the data are not linear.. Part a) is linear; part is non-linear. 4. a), Radius, r (cm) Area, A = πr (cm ).4.56 8.6 4 50.4 5 78.5 6.04. a),, 4. a) 5 0 ( ) 5 5 d) ( 4) e) 8 f) 5 0 g) ( ) h) ( ) 5. a) 5 ( 7) 8 d) ( ) 4 e) 0. 0 f) ( 0.4) quadratic d) 0 cm e) 00 cm 5. a), d) Side Length, s (cm) Surface Area, SA = 6s (cm ) 6 4 54 4 96 5 50 6 6 7 94 8 84 Principles of Mathematics 0: Teacher s Resource Chapter 4 Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
. a) linear BLM 4 9... (page ) neither quadratic e) 40 cm f) Since the data are based on area, there is a squared term in the expression. Section 4. Practice Master. a) quadratic d) neither. a) This is a parabola with x-intercepts and and vertex (0, ). The flight path of the cannonball is a parabola opening downward, starting at an initial height of 0 m, rising to 45 m, and then falling to the ground. x =, (, 45) d) 45 m e) Graph the equation h = 5t + 0t to verify that it passes through the points in the table. The shape of the rope is a parabola opening downward. Principles of Mathematics 0: Teacher s Resource Chapter 4 Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
4. a) Section 4. Practice Master. a) BLM 4 9... (page ) The flight path of the ball is a parabola opening downward, starting at an initial height of 5 m, rising to about 40 m, and then falling to the ground. 40 m d) s 5. a) The flight path of the ball is a parabola opening downward, starting at an initial height of m, rising to just over 4 m, and then falling to the ground. x =.5; points on the left side of the line x =.5 are reflections of points on the right side of the line d) (.5, 4.5) e) 4.5 m f) Test the points in the table in the equation h = x + x +. For example, test the point (, 4): L.S. = h R.S. = x + x + = 4 = () + () + = 4 + 6 + = 4 L.S. = R.S. The point (, 4) is on the parabola h = x + x +. Principles of Mathematics 0: Teacher s Resource Chapter 4 Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
. a) y = x i), ii) Labelled points may vary. Section 4.4 Practice Master BLM 4 9... (page 4). a) Property y = (x ) + vertex (, ) axis of symmetry x = stretch or compression none direction of opening upward values that x may take all real numbers values that y may take y iii) reflection in the x-axis; compression by a factor of i), ii) Labelled points may vary. Property y = ( x+) -- 4 vertex (, 4) axis of symmetry x = stretch or compression vertical compression of factor direction of opening upward values that x may take all real numbers values that y may take y 4 Property y = (x + 4) + vertex ( 4, ) axis of symmetry x = 4 stretch or compression vertical stretch of factor direction of opening downward values that x may take all real numbers values that y may take y iii) reflection in the x-axis; translation of 6 units upward. a) y = x + 5 y = x 9 y = (x 6) d) y = (x + 0) 4. a) y = x y = x y = x d) y = 6x. a) 5. a).5 cm h =.0x +.0 6. a) 86 m m 8 s 7. a =, k = Principles of Mathematics 0: Teacher s Resource Chapter 4 Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
Section 4.5 Practice Master. a) BLM 4 9... (page 5). a) y = (x ) + 4 y = ( x+ ) + y = (x + ) 4 4. a) y = (x + ) y = (x 4) + y = ( x+ ) + 4 5. y = (x + ) + 6. a) 8 m 6 s d) 5.6 m Principles of Mathematics 0: Teacher s Resource Chapter 4 Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
d). a) y = (x + 8)(x ) y = ( x 4)( x 0). a) BLM 4 9... (page 6) 4. a) x = x = 4 x = d) x = 5. a) 75 mg 7.5 mg 9.75 mg 6. a) 8000; 56 000 500 the starting value when measurements were first taken 7. a) 600 years 00 the amount of radium present at t = 0, or now d) the amount of radium present in the past, assuming the model applied 8. a) 800 g 400 g 00 g Chapter 4 Review. a) curve of best fit line of best fit. a) (, 0) one d) y = (x )(x ) 4. a) The data follow a parabola opening upward. $5. a) neither quadratic 5 m 7 m d) 05 m e) 9 m 5. a) 45 m Yes. Section 4.6 Practice Master. a) ( ) d) ( ). a) 6 e) 4 ( ) 4 ( ) e) ( ) ( ) f) 0 000 4 d) 9 f) g) 7 h) 49 64 9. a) 8 4 d) 0 8 linear Principles of Mathematics 0: Teacher s Resource Chapter 4 Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
4. a) d) BLM 4 9... (page 7) 5 m after s 5. a) reflection in the x-axis and vertical stretch by a factor of 6. a) Property y = (x + ) + vertex (, ) axis of symmetry x = stretch or compression none direction of opening upward values that x may take all real numbers values that y may take y translation of units to the left Property y = 4(x 5) vertex (5, ) axis of symmetry x = 5 stretch or compression vertical stretch of factor 4 direction of opening upward values that x may take all real numbers values that y may take y translation of units upward Property y =-- ( x+) -- vertex (, ) axis of symmetry x = stretch or compression vertical compression of factor direction of opening values that x may take values that y may take downward all real numbers y vertical compression by a factor of d) Property y = (x ) 4 vertex (, 4) axis of symmetry x = stretch or compression None direction of opening Downward values that x may take all real numbers values that y may take y 4 Principles of Mathematics 0: Teacher s Resource Chapter 4 Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
7. a) d) BLM 4 9... (page 8) 8. a) $4000 $.50 9. a) Principles of Mathematics 0: Teacher s Resource Chapter 4 Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
7. a) BLM 4 9... (page 9) 0. The data follow a linear pattern. about 58 cm d) Assume that Michael continues to grow at the same rate, following a linear pattern. 8. a) x = compression factor of down d) all real numbers e) y 9. Answers may vary. For example: 40 s 8 000 m. a) 6 64 d) 6 e) f) 5 9 7 g) h) 7 5. a) 5 6 5 6. a) x = x = 4. a) 4 64 4 x = ; 6 0. a) linear Chapter 4 Practice Test. C. D. C 4. B 5. B 6. a) 9 6 d) quadratic Principles of Mathematics 0: Teacher s Resource Chapter 4 Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
. a) Chapter 4 Test. a) BLM 4 9... (page 0). a) 5 m 5 s m 56 m d) 96 m. a), 4, 8, 6,, 64 $ 00 000, $ 600 000, $800 000, $400 000, $00 000, $00 000 Yes. $00 000 4. a) $940 6 d) $70 e) 4 Principles of Mathematics 0: Teacher s Resource Chapter 4 Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
. a) 5. a) quadratic BLM 4 9... (page ) neither linear 6. a) Time, t (h) Radius, r (m) Area, A (m ) 0. 6.6. 0. 4.0 50. 4.7 69.4 4 5.5 95.0 5 6. 4.7 6 7. 67.4 7 7.8 9. 8 8.9 48.8. a) 4 d) 9 4. a) y = (x ) 4 y = (x + ) + Principles of Mathematics 0: Teacher s Resource Chapter 4 Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
8. a =, k = 9. a) 5 mg.5 mg 7.85 mg 0. a) BLM 4 9... (page ) d) 0.4 m; 9.8 m e) 9.7 m ; The areas are very close. The difference may be due to rounding. 7. a) 0 m 0 m d) 605 m The stone follows the path of a parabola opening downward. about 0. m d) about 0.5 s Principles of Mathematics 0: Teacher s Resource Chapter 4 Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited