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)