5.3 Vertex Form of Quadratics 2017.notebook. October 20, Homework Answers:

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Brianna Powers
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1 Homework Answers: a. Vertex (315, 630) b. Domain: (0, 630) Range: (0, 630) c. 360 ft d. 630ft 1

2 Graph WARM UP 1) Find the vertex of the quadratic function: 2) Complete the square on the quadratic above. DO NOT SOLVE. 2

3 5.3 Transforming Parabolas 1) Apply the vertex form to graph a quadratic function. 2) Use vertex form to state vertex and axis of symmetry. Lesson objectives Teachers' notes 3

4 What happens to these graphs?? 4

5 Standard Form y = ax 2 + bx + c What is the vertex of y = x 2 6x + 4? (3, 5) Is x 2 6x + 4 the same as (x 3) 2 5? To graph, you can use the vertex form of quadratic function: y = a(x h) 2 + k where (h,k) is the vertex 5

6 Example 1: y = ½x 2-4x + 13 Axis of symmetry: x = h Vertex: (h, k) Vertex form: y = a(x h) 2 + k 6

7 Sketch the Graph a determines: (1)direction of opening (2)stretch or shrink y = ½(x - 4) Graph 7

8 Example 2: y = (x - 3) 2-5 What is the vertex? What is the axis of symmetry? Now, use the information to draw the graph. Graph 8

9 Example 3: Write a parabola in vertex form with a vertex of ( 5, 6) and a vertical stretch of 2. Graph it! y x

10 Example 4:Write a parabola in vertex form with a vertex of (0, 4) and flipped over the x axis. Graph it! y x

11 Graph Example 5: Vertex: ( 1,6) Convert to Vertex Form y = 2x 2 4x + 4 up or down? down vertical stretch or shrink as compared to the parent function? vertical stretch 11

12 Example 6: Write the equation of the given parabola in vertex form. ( 2, 4) ( 3, 2) Graph 12

13 Example 7: Rewrite the equation in vertex form. 2 Hint: y = a(x - h) + k y = x 2 10x 2 13

14 HOMEWORK HW 5.3 p. 255 #3 48 multiples of 3 Pg 285 #31, 32 14

15 Parabola matching game 15

16 Arrange from tallest to shortest (compared to the parent function) y = ¼(x 1) y = 3(x + 4) 2 10 y = ½(x + 7) 2 1 y = x Taller y = 6(x 2) 2 Shorter 16

17 1 The graph of y = x 2 3 is a parabola with the axis of symmetry given by the equation x = 0. Which of the following coordinates is the point on the parabola that is symmetric to the point ( 1, 2)? A B C D (1, 2) ( 1,2) (1,2) ( 2, 1) 17

18 2 If f(x) = (x 1) 2 + 2, at what value of x is the function f(x) at a minimum? A 1 B 0 C 1 D 2 18

19 3 Use the graph of the given parabola to find each of the following. A Domain? B C D 19

20 4 Use the graph of the given parabola to find each of the following. A Range? B C D 20

21 5 Use the graph of the given parabola to find each of the following. A B Interval of x where f is increasing? C D 21

22 6 Use the graph of the given parabola to find each of the following. A B Interval(s) of x where where f(x) 0? C D 22

23 need a hint? Properties of the graph Domain: set of all possible x-values Range: set of all possible y-values Interval of increasing: interval of x where the y is increasing Interval of decreasing: Instructions interval of x where the y is decreasing 23

24 Fill in the blanks. y = -6(x - 4) 2 y = ¼x 2-4 y = -(x - 1) Direction and width (0, -4) down/basic Vertex (1, 4) y-inter x-inter(s) (0, -4) (0, 5) up/basic down/wide up/narrow Drag this to the target to (0, -96) (4, 0) down/narrow(3, 0) (-1, 0) reveal the answers. (-4, 0) (0, -4) up/wide (4, 0) (0, 3) 24

25 25

Transformations with Quadratic Functions KEY

Transformations with Quadratic Functions KEY Algebra Unit: 05 Lesson: 0 TRY THIS! Use a calculator to generate a table of values for the function y = ( x 3) + 4 y = ( x 3) x + y 4 Next, simplify the function by squaring, distributing, and collecting