X - Intercept

High School

Definition

The points where a curve intersects the x-axis (the horizontal axis on a cartesian plane). Also known as "zero of a function." When a curve intersects the x-axis the value of that point produced by the function is zero. The x-intercept must always be a real number.

Worked examples

\(y = x^2 - 4\) has x-intercepts at \(x = -2\) and \(x = 2\)

Set \(y = 0\) and solve: \(x^2 - 4 = 0\) gives \(x = \pm 2\).

\(f(x) = 2x + 6\) crosses the x-axis at \(x = -3\)

Solve \(2x + 6 = 0\) to find where the line meets the horizontal axis.

\(y = x^2 + 1\) has no x-intercepts

Setting \(x^2 + 1 = 0\) has no real solution, so the parabola never touches the x-axis.

Common mistakes

The x-intercept of \(y = 2x - 6\) is \((3, -6)\) → The x-intercept is \((3, 0)\) At the x-intercept, y is always zero — only the x-coordinate changes.
Writing the x-intercept as just \(y = 0\) → Writing it as \(x = 3\) or the point \((3, 0)\) The x-intercept is the x-value (or coordinate pair) where the curve crosses, not the equation y = 0.
Confusing x-intercept with y-intercept → x-intercept: set \(y = 0\); y-intercept: set \(x = 0\) X-intercept is where the graph crosses the x-axis; y-intercept is where it crosses the y-axis.

Where you'll use it next

You'll use x-intercepts constantly when solving quadratics, graphing polynomials and rational functions, analyzing roots in calculus, and interpreting break-even points in applied algebra and economics.

Found in 2 StudyPug lessons

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