Science, Tech, Math › Math Understanding the X-Intercept of a Quadratic Function Share Flipboard Email Print Thomas Jackson / Getty Images Math Functions Math Tutorials Geometry Arithmetic Pre Algebra & Algebra Statistics Exponential Decay Worksheets By Grade Resources View More By Jennifer Ledwith Math Expert B.B.A., Finance and Economics, University of Oklahoma Jennifer Ledwith is the owner of tutoring and test-preparation company Scholar Ready, LLC and a professional writer, covering math-related topics. our editorial process Jennifer Ledwith Updated October 26, 2019 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 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 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.