1. Find the Product: a. (x – 5)2 b. 4(x +5)(x – 5)

2. A projectile, shot from the ground reaches its highest point of 225 meters after 3.2 seconds. For how manyseconds is the projectile in the air?

ANSWER a. x2 – 10x + 25b. 4x2 – 100

ANSWER 6.4 seconds

Worksheet 4.1 Answers

EXAMPLE 1 Graph a quadratic function in vertex form

Graph y = – (x + 2)2 + 5.14

STEP 1 Identify the constants a = – , h = – 2, and k = 5.

14

STEP 2 Plot the vertex (h, k) = (– 2, 5) and draw the axis of symmetry x = – 2.

EXAMPLE 1 Graph a quadratic function in vertex form

STEP 3 Evaluate the function for two values of x.

x = 0: y = (0 + 2)2 + 5 = 414

–

x = 2: y = (2 + 2)2 + 5 = 114

–

Plot the points (0, 4) and (2, 1) and their reflections in the axis of symmetry.

STEP 4 Draw a parabola through the plotted points.

Because a < 0, the parabola opens down.

You Choose

Get Whiteboards!

Graph the function. Label the vertex and axis of symmetry.

1. y = (x + 2)2 – 3 2. y = –(x – 1)2 + 5

a = 1 vertex is (-2 , -3) a = -1 vertex is (1 , 5)

Choose x values -1 , 0

(-1 , -2) and (0 , 1)

Plot Symmetry Points

(-3 , -2) and (-4 , 1)

Choose x values 2 , 3

(2 , 4) and (3 , 1)

Plot Symmetry Points

(0 , 4) and (-1 , 1)

Line of Symmetry is x = -2 Line of Symmetry is x = 1

EXAMPLE 3 Graph a quadratic function in intercept form

Graph y = 2(x + 3)(x – 1).

STEP 1Identify the x-intercepts. Because p = –3 and q = 1, the x-intercepts occur at the points (–3, 0) and (1, 0).

STEP 2 Find the coordinates of the vertex.

x = p + q2

–3 + 1 2

= –1=

y = 2(–1 + 3)(–1 – 1) = –8

So, the vertex is (–1, –8) and the x-intercepts are (-3, 0) and (1, 0)

Graph the function. Label the vertex, axis of symmetry, and x-intercepts.

5. y = (x – 3)(x – 7) 6. f (x) = 2(x – 4)(x + 1)x-intercepts: (3, 0) and (7, 0)

Vertex: x = (7 + 3)/2 = 5

Vertex: y = (5 – 3)(5 – 7) = -4

Vertex: (5 , -4)

x-intercepts: (4, 0) and (-1, 0)

Vertex: x = [4 + (-1)]/2 = 1.5

Vertex: y = 2(1.5 – 4)(1.5 + 1) = -12.5

Vertex: (1.5 , -12.5)Line of Symmetry: x = 5

Line of Symmetry: x = 1.5

EXAMPLE 5 Change from intercept form to standard form

Write y = –2(x + 5)(x – 8) in standard form.

y = –2(x + 5)(x – 8) Write original function.

= –2(x2 – 8x + 5x – 40) Multiply using FOIL.

= –2(x2 – 3x – 40) Combine like terms.

= –2x2 + 6x + 80 Distributive property

EXAMPLE 6 Change from vertex form to standard form

Write f (x) = 4(x – 1)2 + 9 in standard form.

f (x) = 4(x – 1)2 + 9 Write original function.

= 4(x – 1) (x – 1) + 9= 4(x2 – x – x + 1) + 9 Multiply using FOIL.

Rewrite (x – 1)2.

= 4(x2 – 2x + 1) + 9 Combine like terms.

= 4x2 – 8x + 4 + 9 Distributive property

= 4x2 – 8x + 13 Combine like terms.

GUIDED PRACTICE for Examples 5 and 6

Write the quadratic function in standard form.

9. y = –(x – 2)(x – 7)

–x2 + 9x – 14

11. f(x) = 2(x + 5)(x + 4)

2x2 + 18x + 40

ANSWER ANSWER

10. y = –3(x + 5)2 – 1

–3x2 – 30x – 76

12. f(x) = –(x + 2)2 + 4

–x2 – 4x

ANSWER ANSWER

Classwork Assignment:WS 4.2

(1-29 odd)