1. 6.4 Intercept Form
of Quadratic Functions

2. What is Intercept Form?
Intercept Form –
y = a(x – p)(x – q)
x-intercepts at (p, 0) and (q, 0).
Axis of symmetry
is halfway between
the intercepts.
Example:
y = (x – 3)(x + 1)

3. What are “Zeros”?
The x-intercepts of a function are
also called zeros.
Why?
◦ The function is equal to zero when
x equals those #s.
(-1, 0)
(3, 0)
y = (x – 3)(x + 1)

4. Finding Zeros
To find zeros:
◦ Factor to rewrite in intercept form.
◦ y = ax2 + bx + c y = a(x – p)(x – q)
◦ p and q are the zeros
Example: Find the zeros for
y = x2 – 3x – 4

5. Example:
Find the zeros of y = x2 – x – 6

6. You Try!
Find the zeros of the function
y = x2 + 7x + 12

7. To Graph in Intercept
Form:
1. Plot the x-intercepts.
2. Find the center x value and draw
axis of symmetry.
3. Plug center x value into the
equation to find y.
4. Plot the vertex (x, y).
5. Connect the 3 points with a curve
(parabola).

8. Example:
Graph y = -(x + 2)(x – 4)

9. Example:
Graph

10. You Try!
Graph

11. Example:
Graph y = x2 – 6x + 9

12. Example:
Graph y = 2x2 + 4x – 6

13. You Try!
Graph y = 3x2 + 18x + 24

14. Writing Equations from
Graphs
1. Write intercept form equation,
y = a(x – p)(x – q), replacing p
and q with your intercepts.
2. Plug in the given point (x, y) for
x and y.
3. Solve for a.
4. Rewrite final equation.
Must include x and y!!

15. Example:
Write an equation in intercept
form for the graph shown.

16. Example:
Write an equation of the parabola
with x-intercepts 1 and 4 that
goes through the point (2, -6).

17. Example:
Write an equation in intercept
form for the graph shown.
(-2, -4)

18. You Try!
Write an equation of the
parabola with x-intercepts -2 and
4 that passes through (1, 3).