Understanding the Definition and Steps to Write the X-Intercept in Math

How to write the x-intercept

To write the x-intercept, we need to understand its definition first

To write the x-intercept, we need to understand its definition first.

Definition: The x-intercept is the point on a graph where the curve intersects or crosses the x-axis. It represents the x-coordinate of the point where the graph intersects the x-axis, or in other words, where the y-coordinate is zero.

To write the x-intercept, we follow these steps:

Step 1: Set the equation of the graph equal to zero. This means that we set the y-coordinate to zero, as the x-intercept occurs when the y-coordinate is zero.

Step 2: Solve the equation for the x-values that make the y-coordinate zero. This can be done by performing algebraic operations to isolate the variable x.

Step 3: Express the x-intercept as an ordered pair (x, 0), where the x-coordinate is the value obtained from step 2, and the y-coordinate is always zero since it lies on the x-axis.

Example:

Let’s consider the equation of a quadratic function: y = x^2 + 3x – 4.

Step 1: Set y to zero.

0 = x^2 + 3x – 4

Step 2: Solve the equation.

Factoring or using the quadratic formula, we can find that the solutions are x = -4 and x = 1.

Step 3: Express the x-intercepts as ordered pairs.

The x-intercepts are (-4, 0) and (1, 0).

So, to write the x-intercept, we express it as an ordered pair, where the x-coordinate is the value obtained by solving the equation, and the y-coordinate is always zero since it lies on the x-axis.

More Answers: