1. Warm Up 1. y = 2x – 3 2. 3. y = 3x + 6 4. y = –3x2 + x – 2, when x = 2
Find the x-intercept of each linear function.
1. y = 2x –
3. y = 3x + 6
Evaluate each quadratic function for the given input values.
4. y = –3x2 + x – 2, when x = 2
5. y = x2 + 2x + 3, when x = –1 –2
–12 2

2. Objectives Vocabulary
Find the zeros of a quadratic function from its graph.
Find the axis of symmetry and the vertex of a parabola.
Vocabulary
zero of a function
axis of symmetry

3. Example 1A: Finding Zeros of Quadratic Functions From Graphs
Find the zeros of the quadratic function from its graph. Check your answer.
y = x2 – 2x – 3
y = (–1)2 – 2(–1) – 3
= – 3 = 0
y = 32 –2(3) – 3
= 9 – 6 – 3 = 0
y = x2 – 2x – 3
Check 
The zeros appear to be –1 and 3.

4. Example 1B: Finding Zeros of Quadratic Functions From Graphs
Find the zeros of the quadratic function from its graph. Check your answer.
y = x2 + 8x + 16
Check
y = x2 + 8x + 16
y = (–4)2 + 8(–4) + 16
= 16 – = 0 
The zero appears to be –4.

5. Example 1C: Finding Zeros of Quadratic Functions From Graphs
Find the zeros of the quadratic function from its graph. Check your answer.
y = –2x2 – 2
The graph does not cross the x-axis, so there are no zeros of this function.

6. Example 2a: Finding the Axis of Symmetry by Using Zeros
Find the axis of symmetry of each parabola. A.
(–1, 0)
Identify the x-coordinate of the vertex.
The axis of symmetry is x = –1. B.
Find the average of the zeros.
The axis of symmetry is x = 2.5.

7. Example 3a: Finding the Axis of Symmetry by Using the Formula
Find the axis of symmetry of the graph of
y = –3x2 + 10x + 9.
Step 1. Find the values of a and b.
Step 2. Use the formula.
y = –3x2 + 10x + 9
a = –3, b = 10
The axis of symmetry is

8. Example 3b
Find the axis of symmetry of the graph of
y = 2x2 + x + 3.
Step 1. Find the values of a and b.
Step 2. Use the formula.
y = 2x2 + 1x + 3
a = 2, b = 1
The axis of symmetry is

9. Example 4A: Finding the Vertex of a Parabola
Find the vertex.
y = 0.25x2 + 2x + 3
Step 1 Find the x-coordinate of the vertex. The zeros are –6 and –2.
Step 2 Find the corresponding y-coordinate.
y = 0.25x2 + 2x + 3
Use the function rule.
= 0.25(–4)2 + 2(–4) + 3 = –1
Substitute –4 for x .
Step 3 Write the ordered pair.
(–4, –1)
The vertex is (–4, –1).

10. Example 5
The height of a small rise in a roller coaster track is modeled by f(x) = –0.07x x , where x is the distance in feet from a supported pole at ground level. Find the greatest height of the rise.
Step 1 Find the x-coordinate.
a = – 0.07, b= 0.42
Identify a and b.
Substitute –0.07 for a and 0.42 for b.

11. Example 5 Continued
Step 2 Find the corresponding y-coordinate.
f(x) = –0.07x x
Use the function rule.
= –0.07(3) (3)
Substitute 3 for x.
= 7 ft
The height of the rise is 7 ft.

12. Homework
8.2 Worksheet

13. Lesson Quiz: Part I
1. Find the zeros and the axis of symmetry of the parabola.
2. Find the axis of symmetry and the vertex of the graph of y = 3x2 + 12x + 8.
zeros: –6, 2; x = –2
x = –2; (–2, –4)

14. Lesson Quiz: Part II
3. The graph of f(x) = –0.01x2 + x can be used to model the height in feet of a curved arch support for a bridge, where the x-axis represents the water level and x represents the distance in feet from where the arch support enters the water. Find the height of the highest point of the bridge.
25 feet