How to Find the x-Intercepts of a Function | Step-by-Step Guide & Example

How do you solve for an x intercept?

To solve for an x-intercept, you need to find the value of x when the graph of a function intersects or crosses the x-axis

To solve for an x-intercept, you need to find the value of x when the graph of a function intersects or crosses the x-axis. This means that at the x-intercept, the y-coordinate is zero.

To solve for an x-intercept, follow these steps:

1. Set the function equal to zero by substituting y with zero in the equation. This gives you an equation in terms of x only.
2. Solve the equation for x. This can be done by applying algebraic techniques such as factoring, using the quadratic formula, or simplifying and rearranging the equation.
3. The solutions you obtain will give you the x-values of the x-intercepts.

Let’s work through an example to illustrate this process:

Example: Find the x-intercepts of the quadratic function f(x) = x^2 – 5x + 6.

Step 1: Set the function equal to zero:
0 = x^2 – 5x + 6

Step 2: Solve the equation for x. In this case, we can factor:
0 = (x – 2)(x – 3)

Setting each factor equal to zero:
x – 2 = 0 and x – 3 = 0

Solving these equations gives:
x = 2 and x = 3

So the x-intercepts of the quadratic function are x = 2 and x = 3.

Remember that in some cases, the equation may not factor easily or may not factor at all. In such situations, you can use the quadratic formula (x = [-b ± √(b^2 – 4ac)] / 2a) or other appropriate methods to solve for x.

By finding the x-intercepts, you determine the values of x where the graph of the function intersects the x-axis.

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