Formula to Find x Intercept
Before knowing the formula to find x-intercept, first, we will recall what is x-intercept. The x-intercept of a function is a point(s) where the graph of the function intersects the x-axis. We know that the y-coordinate of every point on the x-axis is 0. We use this to derive the formula to find x-intercept. Let us learn the formula to find the x-intercept along with a few solved examples.
What Is the Formula to Find x Intercept?
The x-intercepts of a function are also called the zeros of the function. Consider a function y = f(x). We already know that:
- The x-intercept(s) is(are) a point(s) where the graph intersects the x-axis.
- If a point lies on the x-axis, its y-coordinate is 0.
Thus, to find the x-intercept of a function, we will just substitute y = 0 in its equation and solve for x value(s). So the formula to find x-intercept is:
If we get the values of x to be \(x_1, x_2, x_3, ...\), then the x-intercepts are \((x_1, 0), (x_2, 0), (x_3, 0),...\). Let us see the applications of the formula to find x-intercept in the following section.
Solved Examples Using Formula to Find x Intercept
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Example 1: Find the x-intercept of the function y = x2 - 7x + 10.
Solution:
To find: The x-intercept of the function y = x2 - 7x + 10.
Using the formula to find x-intercept, to find the x-intercept, we just substitute y = 0 in the given equation and solve for x.
0 = x2 - 7x + 10
0 = (x - 2) (x - 5)
x - 2 = 0; x - 5 = 0
x = 2; x = 5
Answer: The x-intercepts of the given function are (2, 0) and (5, 0)
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Example 2: Use the formula to find the x-intercept of the rational function y = (3x - 1) / (2x + 1).
Solution:
To find: The x-intercept of the given function y = (3x - 1) / (2x + 1).
Using the x-intercept 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 x-intercept of the given rational function is (1 / 3, 0)
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