What is another word for x-intercepts?
The Correct Answer and Explanation is:
Correct Answer:
Another word for x-intercepts is horizontal intercepts.
Explanation:
In mathematics, particularly in the context of graphing functions and equations, the x-intercepts of a graph refer to the points where the graph crosses or touches the x-axis. At these points, the y-coordinate is always zero because the graph lies directly on the horizontal axis.
The term horizontal intercept is often used as a synonym for x-intercept because the x-axis is the horizontal axis on the Cartesian coordinate plane. Both terms describe the same concept but emphasize different perspectives. Saying “x-intercept” highlights the specific axis involved, while “horizontal intercept” emphasizes the orientation of the axis.
To find the x-intercepts of a function, one typically sets the output value, or y, equal to zero and then solves for x. For example, given the quadratic equation
y=x2−4y = x^2 – 4y=x2−4
we find the x-intercepts by solving
0=x2−40 = x^2 – 40=x2−4
This simplifies to
x2=4x^2 = 4×2=4
so
x=2x = 2x=2 or
x=−2x = -2x=−2
Therefore, the graph crosses the x-axis at the points (2, 0) and (–2, 0), which are the x-intercepts or horizontal intercepts.
Understanding x-intercepts is important in many areas of mathematics and science because they often represent the roots or solutions of equations. In real-world applications, they can indicate break-even points in business, zero population growth in biology, or the time when an object hits the ground in physics.
Using the term horizontal intercept is especially helpful for students who are learning to distinguish between the x-axis and y-axis, since it reinforces the idea that the x-axis runs left to right across the graph.
