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Formula to Find x Intercept
Before knowing the formula to find xintercept, first, we will recall what is xintercept. The xintercept of a function is a point(s) where the graph of the function intersects the xaxis. We know that the ycoordinate of every point on the xaxis is 0. We use this to derive the formula to find xintercept. Let us learn the formula to find the xintercept along with a few solved examples.
What Is the Formula to Find x Intercept?
The xintercepts of a function are also called the zeros of the function. Consider a function y = f(x). We already know that:
 The xintercept(s) is(are) a point(s) where the graph intersects the xaxis.
 If a point lies on the xaxis, its ycoordinate is 0.
Thus, to find the xintercept of a function, we will just substitute y = 0 in its equation and solve for x value(s). So the formula to find xintercept is:
If we get the values of x to be \(x_1, x_2, x_3, ...\), then the xintercepts are \((x_1, 0), (x_2, 0), (x_3, 0),...\). Let us see the applications of the formula to find xintercept in the following section.
Solved Examples Using Formula to Find x Intercept

Example 1: Find the xintercept of the function y = x^{2}  7x + 10.
Solution:
To find: The xintercept of the function y = x^{2}  7x + 10.
Using the formula to find xintercept, to find the xintercept, we just substitute y = 0 in the given equation and solve for x.
0 = x^{2}  7x + 10
0 = (x  2) (x  5)
x  2 = 0; x  5 = 0
x = 2; x = 5
Answer: The xintercepts of the given function are (2, 0) and (5, 0)

Example 2: Use the formula to find the xintercept of the rational function y = (3x  1) / (2x + 1).
Solution:
To find: The xintercept of the given function y = (3x  1) / (2x + 1).
Using the xintercept formula, we substitute y = 0 in the above equation and solve for x.
0 = (3x  1) / (2x + 1)
Multiplying both sides by (2x + 1),
0 = 3x  1
x = 1 / 3
Answer: The xintercept of the given rational function is (1 / 3, 0)
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