Quadratic Equation x Intercept

In coordinate geometry, the x intercept means the x-value of the point where the graph of a function or relation intercepts the x-axis of the coordinate system. It means the point at which the line cuts the x-axis.

The x intercept of a line is denoted as (x, 0).

In this article, we are going to learn finding x intercept for the quadratic equation.


Example Problems to Find X Intercept for Quadratic Equation:

Example 1:

Find x intercept for the quadratic equation y = x2 + x - 12

Solution:

Step 1: Given function

y = x2 + x - 12

Step 2: Plug y = 0 in the given function

0 = x2 + x - 12

We can write it as

x2 + x - 12 = 0

Step 3: Solve the above function for x to find x intercept

Find sum of two numbers and its product for x and - 12x2

x = 4x - 3x

-12x2 = (4x)(-3x)

Replace the term x by 4x -3x

x2 + 4x - 3x - 12 = 0

Take the common factor outside,

x(x + 4) - 3(x + 4) = 0

(x + 4)(x - 3) = 0

Factor each term,

x = - 4   and x = 3

Step 4: Solution

X intercepts for the given equation are (- 4, 0) and (3, 0)

Example 2:

Find x intercept for the quadratic equation y = 2x2 + 10x + 8

Solution:

Step 1: Given function

y = 2x2 + 10x + 8

Step 2: Plug y = 0 in the given function

0 = 2x2 + 10x + 8

We can write it as

2x2 + 10x + 8 = 0

Step 3: Solve the above function for x to find x intercept

Find sum of two numbers and its product for 10x and 16x2

10x = 8x + 2x

16x2 = (8x)(2x)

Replace the term 10x by 8x + 2x

2x2 + 8x + 2x + 8 = 0

Take the common factor outside,

2x(x + 4) + 2(x + 4) = 0

(2x + 2)(x + 4) = 0

Factor each term,

x = - 1   and x = - 4

Step 4: Solution

X intercepts for the given equation are (- 1, 0) and (- 4, 0)




Practice Problems to Find X Intercept for Quadratic Equation:

1) Find x intercepts for the quadratic equation y = x2 + 18x + 32

2) Find x intercepts for the quadratic equation y =2 x2 + 14x + 12

2) Find x intercepts for the quadratic equation y = 3x2 + 6x - 8

Solutions:

1) x intercepts are (-2, 0) and (-16, 0)

2) x intercepts are (-1, 0) and (-6, 0)

3) x intercepts are (0.914, 0) and (-2.914, 0)