1. Warm Up #2 Find the Product: a. (x – 5)2 b. 4(x +5)(x – 5) ANSWER
A projectile, shot from the ground reaches its highest
point of 225 meters after 3.2 seconds. For how many
seconds is the projectile in the air?
ANSWER
6.4 seconds

2. Worksheet 4.1 Answers

4. EXAMPLE 1
Graph a quadratic function in vertex form 14
Graph y = – (x + 2)2 + 5.
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.

5. 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 = 4 14 –
You Choose
x = 2: y = (2 + 2)2 + 5 = 1 14 –
Plot the points (0, 4) and (2, 1) and their reflections in the axis of symmetry.
Because a < 0, the parabola opens down.
STEP 4
Draw a parabola through the plotted points.

6. Get Whiteboards!

7. 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)
Line of Symmetry is x = 1
Line of Symmetry is x = -2
Choose x values 2 , 3
Choose x values -1 , 0
(2 , 4) and (3 , 1)
(-1 , -2) and (0 , 1)
Plot Symmetry Points
Plot Symmetry Points
(0 , 4) and (-1 , 1)
(-3 , -2) and (-4 , 1)

9. EXAMPLE 3
Graph a quadratic function in intercept form
Graph y = 2(x + 3)(x – 1).
STEP 1
Identify 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 + q 2
–3 + 1
= –1 =
y = 2(–1 + 3)(–1 – 1) = –8
So, the vertex is (–1, –8) and the x-intercepts are (-3, 0) and (1, 0)

10. 5. y = (x – 3)(x – 7) 6. f (x) = 2(x – 4)(x + 1)
Graph the function. Label the vertex, axis of symmetry, and x-intercepts.
5. y = (x – 3)(x – 7)
f (x) = 2(x – 4)(x + 1)
x-intercepts: (3, 0) and (7, 0)
x-intercepts: (4, 0) and (-1, 0)
Vertex: x = (7 + 3)/2 = 5
Vertex: x = [4 + (-1)]/2 = 1.5
Vertex: y = (5 – 3)(5 – 7) = -4
Vertex: y = 2(1.5 – 4)( ) = -12.5
Vertex: (5 , -4)
Vertex: (1.5 , -12.5)
Line of Symmetry: x = 5
Line of Symmetry: x = 1.5

12. Change from intercept form to standard form
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

13. Change from vertex form to standard form
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
Rewrite (x – 1)2.
= 4(x2 – x – x + 1) + 9
Multiply using FOIL.
= 4(x2 – 2x + 1) + 9
Combine like terms.
= 4x2 – 8x
Distributive property
= 4x2 – 8x + 13
Combine like terms.

14. GUIDED PRACTICE
for Examples 5 and 6
Write the quadratic function in standard form.
9. y = –(x – 2)(x – 7)
f(x) = 2(x + 5)(x + 4)
ANSWER
ANSWER
–x2 + 9x – 14
2x2 + 18x + 40
10. y = –3(x + 5)2 – 1
f(x) = –(x + 2)2 + 4
ANSWER
ANSWER
–3x2 – 30x – 76
–x2 – 4x

16. Classwork Assignment: WS 4.2 (1-29 odd)