Quadratics in Vertex Form Unit 1

Transcription

1 1 U n i t 1 11C Date: Name: Tentative TEST date Quadratics in Verte Form Unit 1 Reflect previous TEST mark, Overall mark now. Looking back, what can ou improve upon? Learning Goals/Success Criteria Use the following checklist to help ou determine what ou know well and where ou need additional review. I kind of No, I get it. I DAYS cannot. don t get & Can ou I need to the right Pages learn this. answers ver often. I get it. I could work on being more consistent. Yes, I can. I have perfected this! Recognize a quadratic relation from an equation? Da 1 Pg -3 Recognize a quadratic relation from a graph? Recognize a quadratic relation from a table of values? Identif the ke features of a quadratic (zeros, -intercept, verte, ais of smmetr and optimal value) from it's graph? Graph and summarize the ke features of the basic parabola ( = ) Da Pg 4-5 Da 3 Pg 6 Da 4 Pg 7 Da 5 Pg8-9 Da 6 Pg10-11 Da 7 Pg1-15 Describe how transformations (reflection, vertical stretch/compression, horizontal or vertical translation) affect the basic parabola? Identif transformations applied to = b looking at an equation in verte form and/or it s graph. Create the equation of a quadratic in verte form given information about the transformations applied to =. Create the equation of a quadratic in verte form given the graph of the parabola. Recognize the equation of a quadratic in verte form? Identif the verte, ais of smmetr and optimal value of a quadratic from it's equation (in verte form)? Sketch a parabola in verte form (a transformed parabola)? Use the equation of a quadratic relation which models a real-life situation to answer questions in the contet of the problem? Use information from a real-life situation to model a quadratic relation (create an equation or graph or table of values)? REVIEW 1

2 U n i t 1 11C Date: Name: DAY 1 Modelling Quadratic Relations 1. Use the mathematical models to determine whether the relation is linear, quadratic or neither (circle the appropriate answer). Give a reason for each answer. a. = b. 1 st nd 4 5 c. linear or quadratic or neither? Reason: d. = 6 linear or quadratic or neither? Reason: linear or quadratic or neither? Reason: e. 1 st nd linear or quadratic or neither? Reason: linear or quadratic or neither? Reason: f. linear or quadratic or neither? Reason:. Last ear a clothing boutique sold 100 t-shirts for $10 each. Market research suggests that for ever $5 increase in price, 00 fewer t-shirts will be sold. a. Complete the table until the price is $40 in the table below. b. Graph the data below. Plot Price against Income. Label aes and give graph a title. Price Number of T- shirts Sold Income $ $1 000 $ $0 $5 $30 $35 $40 c. Which price results in the maimum income?

3 3 U n i t 1 11C Date: Name: ht= 3. A cannonball is shot horizontall from the top of a cliff. Its path can be modelled b the relation, where h is the cannonball's height above the ground, in metres, and t is the time, in seconds. a. Complete the table below. time h = 150 5t height 1 st nd b. Is the relation quadratic? How do ou know? c. Graph the relation in the grid above. Label aes and give graph a title. 4. A craft store sold 800 ornaments for $ each. A surve suggests that ever $1 increase in price will reduce sales b 100. a. Complete the table below until no ornaments are sold. b. Graph the data Price versus Income. Label aes and give graph a title. Price Number of Ornaments Sold Income c. Which price results in the maimum income? 3

4 4 U n i t 1 11C Date: Name: DAY Changing Quadratic Relations: The Value of 'a' 1. State the verte and the maimum or minimum value for each parabola. a. b. c. Verte: ma or min?: Verte: Ma or Min?: Verte: Ma or Min?:. State the ke features of each graph. zeros -intercept verte ais of smmetr optimal value 4

5 5 U n i t 1 11C Date: Name: 3. For each of the following, state how the value of a is affecting the basic parabola (compression, stretch and/or reflection). The basic parabola, =, is shown with a dotted line. a. b. c. d. 4. State the transformations and graph each of the following parabolas. a. = b. = 1 / 3 (I) TRANSFORMATIONS (II) GRAPH 5. For each set of quadratics, circle the one that is wider a. = 0. = 5 b. = 3 c. = 5 = 0.4 = d. e. f. = 0.1 = 0. = 0.9 = 0.5 = 0.03 = 0.4 5

6 6 U n i t 1 11C Date: Name: DAY 3 Changing Quadratic Relations: The Values of 'h' and 'k' 1. For each of the following, state how the value of h and/or k is affecting the basic parabola horizontal (left/right) or vertical (up/down) translation. The basic parabola, =, is shown with a dotted line. a. b. c. d.. State the transformations and graph each of the following parabolas. a. = ( 1) + b. = ( + 3) 4 (I) TRANSFORMATIONS (II) GRAPH 3. For each set of quadratics, circle the one that has it's verte farther from the -ais. a. = + 5 = 4 b. = + = 3 4. For each set of quadratics, circle the one that has it's verte farther from the -ais. a. = ( + 3) = ( ) b. = ( 1) = ( ) 6

7 7 U n i t 1 11C Date: Name: DAY 4 Creating an Equation in Verte Form 1. State the equation for each of the following parabolas. a. b. c. A parabola has a verte (5, ) and passes through the point (1, 4). d. A parabola has a verte ( 3, 6) and a - intercept of 1. 7

8 8 U n i t 1 11C Date: Name: DAY 5 Verte Form of Quadratic Relations: = a( h) + k 1. For each of the following quadratic relations in verte form, (i) state the transformations, (ii) graph the parabola, and (iii) state the ke features. = ( 4) + 5 = 1 / 3( + ) 4 (I) TRANSFORMATIONS (II) GRAPH zeros zeros (III) KEY FEATURES -intercept verte ais of smmetr -intercept verte ais of smmetr optimal value optimal value 8

9 9 U n i t 1 11C Date: Name:. Collect the following information for each quadratic in verte form. The first one is done. Transformations Equation a h k verte ais of smmetr optimal value ( ) = reflection stretch b 7 left 4 up 10 ( 4, 10) = 4 =10, ma ( ) = 3 5 ( ) = ( ) = ( ) 1 = ( ) = ( ) = ( ) = 4 3 ( ) = ( ) = ( ) 1 =

10 10 U n i t 1 11C Date: Name: DAY 6 Understanding Problems Involving Quadratic Relations 1. The manager of a hocke arena is pricing tickets for an upcoming game. She knows that if she increases the R = 100 P , ticket price she will sell fewer tickets. The situation is modelled b the relation ( ) where R is the total revenue and P is the ticket price, both in dollars. a. Create a table of values and graph the relation. Label aes and give graph a title. b. What is the verte of the parabola? c. What do the coordinates of the verte represent in this situation?. The Windsor-Detroit International Freedom Festival hosts one of the largest fireworks displas in the world. The fireworks are set off over the Detroit River. The path of a particular firework rocket is modelled b the relation ( ) h = 4.9 t , where h is the rocket's height above the water, in metres, and t is the time, in seconds. a. How long will the rocket take to reach its maimum height? b. What is the maimum height? c. A firework rocket will sta lit for an average of 5 s. What will the height of a rocket be 5 s after it is launched? 10

11 11 U n i t 1 11C Date: Name: 3. The shape of a satellite dish is parabolic. the dish is 5 cm deep and 40 cm wide. a. Sketch the parabola opening up. Label aes and give graph a title. b. Write a relation of the form = a( h) + k that models the shape of this dish. The point (1, 0.015) is also on the parabola. 11

12 1 U n i t 1 11C Date: Name: REVIEW 1. A rectangular swimming area is to be enclosed b 60 m of rope. One side of the swimming area is along the shore so the rope will onl be used on three sides. The graph shows how the swimming area is related to the length of the side perpendicular to the beach. a. Interpret what the verte represents. Draw a sketch this swimming area and label it. b. What are the dimensions of the largest swimming area? c. Draw the swimming areas that correspond to points A and B, and label their dimensions. What is the same about these swimming areas? Which would ou prefer, and wh? 1

13 13 U n i t 1 11C Date: Name:. The stopper in a bathtub is released and the water begins to drain. The volume of water, V litres, in the tub t minutes after the stopper is pulled is given b the equationv = 5t 8t a. Complete the table to graph the relation. Label aes and give graph a title. t 5t 8t + 10 V Wh do we onl need to use the first quadrant? b. How man litres of water are in the tub when it begins to drain? c. How much time does it take for all the water to drain? 3. (i) State the transformations to = for each of the following and (ii) sketch each graph. a. = ( ) b. = (I) TRANSFORMATIONS (II) GRAPH 13

14 14 U n i t 1 11C Date: Name: a. = b. = + (I) TRANSFORMATIONS (II) GRAPH a. How are the graphs the same? b. How are the different? 4. In each case, the parabola = a( h) + k. = is transformed as described. Write the equation of the new parabola in the form a. The parabola is translated units up and 5 units right. b. The parabola is stretched verticall b a factor of 4. c. The parabola is translated units right, then reflected in the -ais. d. The parabola is compressed verticall b a factor of

15 15 U n i t 1 11C Date: Name: 5. Match each parabola with its equation. Eplain our answers. 1 Equation Matches Graph Number Because... ( ) = = 6. Use the graph of a quadratic relation below to determine it`s equation. 15