How to find the x-intercept of a quadratic function?

The x-intercept of a line is that point where it cuts the x-axis of the graph, and the y-intercept of a line is that point where it cuts the y-axis of the graph.

Answer: To find the x-intercept of a line, we substitute y = 0 in the equation and find the corresponding value of x.

Let us proceed step by step.

Explanation:

There are few steps to determine the x-intercept of a quadratic function.

• Step 1: Put the value of y as 0.
• Step 2: Solve the equation and get the two roots x₁ and x₂.
• Step 3: Write x-intercept as (x₁ , 0) and (x₂ , 0) 

Let's understand the problem with the help of an example.

Let's find the x-intercepts of y = x² - 5x + 6

To find the x-intercept, put y = 0.

Hence, x² - 5x + 6 = 0

x² - 5x + 6 = (x - 3) (x - 2) = 0

Therefore, x₁ = 3 and x₂ = 2.

The x-intercepts of y = x² - 5x + 6 is (2, 0) and (3, 0). 

Hence, to find the x-intercept of a line, we substitute y = 0 in the equation and find the corresponding value of x.