1. Objectives Vocabulary zero of a function axis of symmetry
Find the zeros, axis of symmetry, vertex and range of a quadratic function from its graph.
Find the axis of symmetry and the vertex of a parabola given an equation.
Vocabulary
zero of a function
axis of symmetry

2. NOTES
Find the A) the zeros B) the axis of symmetry C) the vertex D) and the range of the parabola.
2. Find the axis of symmetry and the vertex of the graph of y = 3x2 + 12x + 8.

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
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
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. A vertical line that divides a parabola into two symmetrical halves is the axis of symmetry. The axis of symmetry always passes through the vertex of the parabola. You can use the zeros to find the axis of symmetry.

8. Example 2
Find the axis of symmetry and the vertex of each parabola. a.
The axis of symmetry is x = –3.
The vertex is (-3, 0) b.
The axis of symmetry is x = 1.
The vertex is (1, 5)

9. If a function has no zeros or they are difficult to identify from a graph, you can use a formula to find the axis of symmetry. The formula works for all quadratic functions.

10. Once you have found the axis of symmetry, you can use it to identify the vertex.

11. Example 3A: Finding the Vertex of a Parabola
Find the vertex.
y = –3x2 + 6x – 7
Step 1 Find the x-coordinate of the vertex.
a = –3, b = 6
Identify a and b.
Substitute –3 for a and 6 for b.
The x-coordinate of the vertex is 1.

12. Example 4B Continued
Find the vertex.
y = –3x2 + 6x – 7
Step 2 Find the corresponding y-coordinate.
y = –3x2 + 6x – 7
Use the function rule.
= –3(1)2 + 6(1) – 7
Substitute 1 for x.
= –3 + 6 – 7
= –4
Step 3 Write the ordered pair.
The vertex is (1, –4).

13. Example 3B
Find the vertex.
y = x2 – 4x – 10
Step 1 Find the x-coordinate of the vertex.
a = 1, b = –4
Identify a and b.
Substitute 1 for a and –4 for b.
The x-coordinate of the vertex is 2.

14. Example 3B Continued
Find the vertex.
y = x2 – 4x – 10
Step 2 Find the corresponding y-coordinate.
y = x2 – 4x – 10
Use the function rule.
= (2)2 – 4(2) – 10
Substitute 2 for x.
= 4 – 8 – 10
= –14
Step 3 Write the ordered pair.
The vertex is (2, –14).

15. NOTES
Find the A) the zeros B) the axis of symmetry C) the vertex D) and the range 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
Vertex (-2, -16)
Range: y > -16
x = –2; (–2, –4)