Algebra 2 Honors. Unit 4, Day 1 Period: Date: Graph Quadratic Functions in Standard Form. (Three more problems on the back )

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1 Algebra Honors Name: Unit 4, Day 1 Period: Date: Graph Quadratic Functions in Standard Form 1. y = 3x. y = 5x y = x 5 4. y = 1 5 x 6. y = x + x f(x) = 6x 4x 5 (Three more problems on the back )

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3 Algebra Honors Name: Unit 4, Day Graph Absolute Value Functions Period: Date: Graph the following absolute value functions 1. y x 5. y x 5 3. y x 4 6. y x y 4 x 3 (More Questions on the back )

4 6. Write the equation of the absolute value function that is translated right 3 units and down. 7. Write the equation of the absolute value function that is reflected across the x axis, vertically shrunk by a factor of 1/3 and is translated up Given the equation y x 4, if this graph was translated up 9 units and left 7, what is the equation of the new graph? 9. Given the equation y 1 x, if this graph was reflected across the x-axis, translated down 3 units and right 7, what is the equation of the new graph?

5 Algebra Honors Name: Unit 4, Day 3 Period: Date: Graph Quadratic Functions in Vertex Form 1. y = (x 3). f(x) = (x + 3) f(x) = (x 1) 5 4. y = 1 (x 3) +

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7 Honors Algebra Name: UNIT 4, Day 4 Period: Date: Graph Quadratic Functions in Vertex Form and Standard Form Write the following functions in vertex form. 1. y x x 6 1. h x x x ( ) Graph the following quadratic functions. Label the vertex, the axis of symmetry, and state the domain and range. 3. y.5( x 4) 3 4. y x x y x x g x x x ( )

8 Graph the following quadratic functions. Label the vertex, the axis of symmetry, state the domain and range, and identify the end behavior of the graphs. f x 3 x 1 Compare this graph with the parent function, and then state the domain and range. Comparison: 7. Increasing: Positive: Decreasing: Negative: Zeroes: Minimum or Maximum (what is it?): f( x) as x and f( x) as x 8. g( x) x 8x 97 Compare this graph with the parent function, and then state the domain and range. Comparison: Increasing: Positive: Decreasing: Negative: x-intercepts: Minimum or Maximum (what is it?): gx ( ) as x and gx ( ) as x 9. f x x 3 Compare this graph with the parent function, and then state the domain and range. Comparison: Increasing: Positive: Decreasing: Negative: x-intercepts: Minimum or Maximum (what is it?): f( x) as x and f( x) as x

9 Algebra Honors Name: Unit 4, Day 5 Graph Absolute Value Functions Period: Date: Without graphing, identify the name of the parent function and the general shape of the parent function graph. Then describe how the graph of the given function will be transformed from the parent graph. 1. y x 1. y ( x 3) 1 Name of parent: Name of parent: General Shape: Transformation: General Shape: Transformation: 3 3. y x y 4( x 4) 5 3 Name of parent: Name of parent: General Shape: Transformation: General Shape: Transformation: Describe the transformation upon the graph f x 5. g x ( 4) 3 5 h x 7. g x 4 8.

10 Use the notation above to communicate the transformations of the graphs below. The original graph is the parent function graph, which goes through the origin

11 Honors Algebra Name: Unit 4, Day 6 Graph Quadratic Functions Intercept Form Period: Date: Write the following functions in intercept form. 1. y x x 6 9. f ( x) x 9x 4 3. h x ( ) 9x 49 Graph the following quadratic functions. Label the vertex, the axis of symmetry, and state the domain and range. 4. f x ( x 3)( x 1) 5. y.5( x 4)( x ) Zeros: Solutions: 6. y x x 6 5 x-intercepts:

12 Graph the following quadratic functions. Label the vertex, the axis of symmetry, state the domain and range, and identify the end behavior of the graphs f x x 1 ( x 3) 8. g x ( x )( x 1) x-intercepts: Zeros: f( x) as x and f( x) as x gx ( ) as x and gx ( ) as x 9. f ( x) x 6x Solutions: f( x) as x and f( x) as x

13 Honors Algebra Name: Unit 4, Day 7 Changing Forms of a Quadratic Function Period: Date: Write the following functions in standard form. 1. y ( x 1) 7 Write the following functions in standard form.. y 5( x 1) x Write the following functions in vertex form. 3. y 3( x 4) x 4. f x x x ( ) 7 6 Write the following functions in intercept form. 5. y x f x x x ( ) Write a parabola that has a vertex at (0, 1) and is vertically stretched by a factor of in vertex form. 8. Write a parabola that has roots at 3 and 7, is vertically shrunk by a factor of ½, and is reflected over the x- axis in standard form. 9. Write a parabola that has a vertex at the ( 1, 8) is vertically stretched by a factor of in intercept form.

14 Graph the following quadratic functions. Label the vertex, the axis of symmetry, state the domain and range, and identify the end behavior of the graphs f x x 11. g x x( x ) x-intercepts: Zeros: f( x) as x and f( x) as x gx ( ) as x and gx ( ) as x 1. f x x x ( ) 6 5 Solutions: f( x) as x and f( x) as x

15 Honors Algebra Name: Unit 4, Day 8 Application of Quadratics Period: Date: Kim wants to buy a used car with good gas mileage. He knows that the miles per gallon, or mileage, vary according to various factors, including the speed. He finds that highway mileage for the make and model he wants can be approximated by the function f(s) 0.03s.4s 30, where s is the speed in miles per hour. He wants to graph this function to estimate possible gas mileages at various speeds. 1. Determine whether the graph opens upward or downward.. Identify the axis of symmetry for the graph of the function. 3. Find the y-intercept. 4. Find the vertex. 5. Graph the function. 6.a. Does the curve have a maximum or a minimum value? b.what is the value of the y-coordinate at the maximum or minimum? c. Explain what this point means in terms of gas mileage. A ball is hit into the air from a height of 4 feet. The function g( t) 16t 10t 4 can be used to model the height of the ball where t is the time in seconds after the ball is hit. Choose the letter for the best answer. 7. About how long is the ball in the air? A. 3.5 seconds B seconds C. 7 seconds D. 7.5 seconds What is the maximum height the ball reaches? A. 108 feet B. 14 feet C. 9 feet D. 394 feet

16 Sean and Mason run out of gas while fishing from their boat in the bay. They set off an emergency flare with an initial vertical velocity of 30 meters per second. The height of the flare in meters can be modeled by t h( t) , where t represents the number of seconds after launch. 9. Sean thinks the flare should reach at least 15 meters to be seen from the shore. So let s help them to see if they will be saved. a. How high will the flare reach? b. How long will it take to reach that height? c. Mason thinks that the flare will reach 15 meters in 5.4 seconds. Is he correct? Explain. d. Sean thinks the flare will reach 15 meters sooner, but then the flare will stay above 15 meters for about 5 seconds. Is he correct? Explain. e. How far will the flare travel before it hits the water? 10. The boys fire a similar flare from the deck 5 meters above the water level. Which statement is correct? A The flare will reach 45 m in 3 s. B The flare will reach 50 m in 3 s. C The flare will reach 45 m in 3.5 s. D The flare will reach 50 m in 3.5 s. 11. In the problem above, what effect does the deck have on the graph of the flare. What would this change?

17 Erin and her friends launch a model rocket from ground level vertically into the air with an initial velocity of 80 feet per second. The height of the rocket, () h( t) 16t t 5. ht, after t seconds is given by 1. They want to find out how high they can expect the rocket to go and how long it will be in the air. a. How long will the entire flight of the rocket last? b. Find the number of seconds the rocket will be in the air before it starts its downward path. c. How high can they expect their rocket to go? 13. Megan gets ready to launch the same rocket from a platform 1 feet above the ground with the same initial velocity. a. Write a function in standard form that represents the rocket s path for this launch. b. Factor the corresponding equation to find the values for t when h is zero. c. Erin says that the roots of the equation are t 5.5 and t 0.5 and that the rocket will stay in the air 5.5 seconds. Megan says she is wrong. Who is correct? How do you know? Choose the letter for the best answer. 14. Which function models the path of a rocket that lands 3 seconds after launch? A. B. C. D. h t t t ( ) h t t t ( ) h t t t ( ) h t t t ( ) Megan reads about a rocket whose path can be h( t) 16 t 3 t 1 modeled by the function Which could be the launch height? A. 16 ft off the ground B. 48 ft off the ground C. 3 ft off the ground D. 4 ft off the ground

18 17. A stuntwoman jumps from a building 73ft high and lands on an air bag that is 9ft tall. Her height above ground h in feet can be modeled by h (t) = t, where t is the time in seconds. a. How many seconds will the stuntwoman fall before touching the air bag? (Hint: Find the time t when the stuntwoman s height above ground is 9 ft.) b. Suppose the stuntwoman jumps from a building that is half as tall. Will she be in the air for half as long? Explain. 18. A baseball player hits a ball toward the outfield. The height h of the ball in feet is modeled by h( t) 16t t 3 where t is the time in seconds. In addition, the function d (t) = 85t models the horizontal distance d traveled by the ball. a. If no one catches the ball, how long will it stay in the air? b. What is the horizontal distance that the ball travels before it hits the ground? 19. The height h in feet of a baseball hit from home plate can be modeled by the function h( t) 16t 3t 5.5, where t is the time in seconds since the ball was hit. The ball is descending when it passes 7.5ft over the head of a 6ft player standing on the ground. a. To the nearest tenth of a second, how long after the ball is hit does it pass over the player s head? b. The horizontal distance between the player and home plate is 10 ft. Use your answer from part a to determine the horizontal speed of the ball to the nearest foot per second.