An x-intercept is a point where a graph crosses or touches the x-axis. Its y-coordinate is always 0, so it is written (a, 0). To find it, set y = 0 and solve for x. A non-horizontal line has one x-intercept, while a parabola can have two, one or none.
The x-intercept is where the graph meets the x-axis, so y = 0 there. For 2x + 3y = 6, it is (3, 0).
Formal definition and notation
An x-intercept of the graph of an equation in x and y is a point (a, 0) on the graph, that is, a point where y = 0. For the graph of a function y = f(x), the x-intercepts are the points (a, 0) with f(a) = 0; their x-coordinates are the real zeros of f and the real solutions of the equation f(x) = 0.
Symbol
Read it as
Meaning
(a, 0)
a comma zero
the x-intercept as a point; often the answer is given as just x = a
The y-intercept is where the graph crosses the y-axis, at x = 0: for 2x + 3y = 6 it is (0, 2). The x-intercept has y = 0: (3, 0).
X-Interceptvs.Zero of a function
A zero is the input number a with f(a) = 0, such as 3. The x-intercept is the point (3, 0) on the graph. They carry the same information.
Quick check: 3 questions
Question 1 of 3
What is the x-intercept of 5x − 2y = 15?
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Answer: B. Set y = 0: 5x = 15, so x = 3, giving (3, 0). (0, −7.5) is the y-intercept, (−3, 0) has a sign error, and (0, 3) puts the value in the wrong coordinate.
Question 2 of 3
How many x-intercepts does y = (x − 2)2 have?
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Answer: C.(x − 2)2 = 0 only when x = 2, so the vertex (2, 0) just touches the axis: one x-intercept. Two would need two different solutions, and none would need the parabola to stay off the axis.
Question 3 of 3
A line has slope 3 and y-intercept (0, −12). Where is its x-intercept?
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Answer: D. The line is y = 3x − 12. Setting y = 0 gives x = 4, so (4, 0). (−4, 0) has the wrong sign, (−36, 0) multiplied instead of dividing, and (0, 4) is on the y-axis.
X-Intercept: frequently asked questions
How do you find the x-intercept of an equation?
Replace y with 0 and solve the equation that is left for x. For y = 2x + 8, 0 = 2x + 8 gives x = −4, so the x-intercept is (−4, 0). On a graph, look for the points where the curve meets the horizontal axis and read their x-values.
Can a graph have more than one x-intercept?
Yes. A non-horizontal line has exactly one, but curves can have several. A parabola can have two, one or none, and a cubic such as y = x3 − 4x has three: at x = −2, 0 and 2. A circle centered at the origin crosses the x-axis twice.
Is the x-intercept the same as a root or zero?
Almost. A root or zero is the x-value that makes the function equal 0, such as x = 3. The x-intercept is the point on the graph, (3, 0). Only real zeros appear as x-intercepts; complex roots of a quadratic do not show up on the graph at all.
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The two axes divide the plane into four quadrants, numbered I to IV counterclockwise from the upper right.Geometry · Grade 5, Grade 6, Grade 7Ordered PairAn ordered pair is two numbers written to locate a point on the coordinate plane. It is written as (x, y): the x-value comes first, and the y-value comes second. From the origin, move x units across, then y units up or down. The order matters: (2, 5) and (5, 2) are different points.Geometry · Grade 5, Grade 6, Grade 7Standard Form of a Linear EquationThe standard form of a linear equation is Ax + By = C, where A, B and C are integers and A and B are not both 0. Both variables sit on the left side. It makes the intercepts easy to find: the x-intercept is CA, the y-intercept is CB, and the slope is −AB.Algebra · Grade 8, Algebra 1Slope-Intercept FormSlope-intercept form is the linear equation form y = mx + b, where m is the slope and b is the y-intercept. 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