x-intercept

Topic

Quadratics Concepts

Definition

The x-intercept of a function is the point where the graph intersects the x-axis, indicating the value of x when f(x) = 0.

Description

The x-intercept is a critical concept in understanding the solutions of quadratic functions. It is defined as the point(s) at which the graph of a function intersects the x-axis, meaning the output value (y) is zero. For a quadratic function expressed in the standard form 

f(x) = ax² + bx + c

the x-intercepts can be found through factoring, completing the square, or using the quadratic formula. In real-world applications, the x-intercept is significant as it often indicates key values such as roots of equations in physics, economics, and engineering contexts. For instance, in the context of projectile motion, finding the x-intercept helps determine when an object will hit the ground. In math education, understanding x-intercepts facilitates students’ ability to graph quadratic functions accurately and comprehend the significance of roots. 

An example illustrating this is finding the x-intercepts of the function 

f(x) = x² − 4

which can be solved to find roots at x = − 2 and x = 2.

For a complete collection of terms related to Quadratic Expressions, Functions, and Equations click on this link: Quadratics Collection