Understanding the X-Intercept of a Quadratic Function

Hand elevating graph line off the page
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The graph of a quadratic function is a parabola. A parabola can cross the x-axis once, twice, or never. These points of intersection are called x-intercepts. Before tackling the subject of the x-intercept, students should be able to confidently plot ordered pairs on a Cartesian Plane.

X-intercepts are also called zeros, roots, solutions, or solution sets. There are four methods for finding x-intercepts: the quadratic formula, factoring, completing the square, and graphing.

A Parabola With Two X-intercepts

Use your finger to trace the green parabola in the image in the next section. Notice that your finger touches the x-axis at (-3,0) and (4,0). Therefore, the x-intercepts are (-3,0) and (4,0).

Note that the x-intercepts are not merely -3 and 4. The answer should be an ordered pair. Note also that the y-value of these points is always zero.

A Parabola With One X-Intercept

Parabola with one root
Krishnavedala/Wikimedia Commons/Creative Commons 3.0

Use your finger to trace the blue parabola in the image in this section. Notice that your finger touches the x-axis at (3,0). Therefore, the x-intercept is (3,0).

A question to ask to check your understanding is, "When a parabola has only one x-intercept, is the vertex always the x-intercept?"

A Parabola Without X-Intercepts

Parabola with no x intercept
Olin/Wikimedia Commons/Creative Commons 3.0

Use your finger to trace the blue parabola in this section. Note that your finger does not touch the x-axis. Therefore, this parabola has no x-intercepts.