Quadratic X-Intercepts Sample Problems

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Quadratic X-Intercepts

For this topic, you will need to know how to factor quadratic equations.
To review, the following topics will help:

An x-intercept is the x-coordinate of the point where a graph intersects the x-axis (also the y = 0 line). Graphs of quadratic equations can have two, one, or no x-intercepts.

To find the x-intercepts of a quadratic equation f(x) = ax² + bx + c,

1. Set the equation to zero.
0 = ax² + bx + c
2. Use factoring or the quadratic formula to solve for x.

Example 1: Factoring

Find the x-intercepts of each function. Separate multiple answers by commas. Example: x=-3/2,2
If there is no x-intercept, write "none".
f(x) = x² + 7x + 12 x-intercepts:
Set the equation equal to zero and factor.

x² + 7x + 12 = 0

(x + 3)(x + 4) = 0

Solve for x.

x + 3 = 0 x + 4 = 0

x = -3 x = -4

Therefore, the x-intercepts are -3 and -4.
x-intercepts: