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

2. Recall that an x-intercept of a function is a value of x when y = 0
Recall that an x-intercept of a function is a value of x when y = 0. A zero of a function is an x-value that makes the function equal to 0. So a zero of a function is the same as an x-intercept of a function. Since a graph intersects the x-axis at the point or points containing an x-intercept, these intersections are also at the zeros of the function. A quadratic function may have one, two, or no zeros.

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.

7. Find the axis of symmetry of each parabola.
(–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.

8. Y= x2 + 4x - 21
Check Graph the related quadratic function. The zeros of the related function should be the same as the solutions from factoring. ●
The graph of y = x2 + 4x – 21 shows that two zeros appear to be –7 and 3, the same as the solutions from factoring. 

9. Check Graph the related quadratic function.
Y= x2 – 12x + 36
Check Graph the related quadratic function. ●
The graph of y = x2 – 12x + 36 shows that one zero appears to be 6, the same as the solution from factoring. 

10. Y=x2 + 4x - 5
Check Graph the related quadratic function. The zeros of the related function should be the same as the solutions from factoring. ●
The graph of y = x2 + 4x – 5 shows that the two zeros appear to be 1 and –5, the same as the solutions from factoring. 