FreeAlgebra                             Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# The Intercepts of a Parabola

Example 1

Find the y- and x-intercepts of the function: f(x) = x2 - 4x + 4

Solution

The y-intercept is the point where x = 0. It is the point (0, C). For the given function, it is (0, 4).

To find the x-intercepts, replace f(x) with 0 and then solve for x.

 Original function. Substitute 0 for f(x). f(x) = x2 - 4x + 4 0 = x2 - 4x + 4

To solve for x

 Factor. Set each factor equal to 0. Solve each equation. 0 x - 2 x = (x - 2)(x + 2)= 0 or x - 2 = 0 = 2 or x = 2

We have one solution, x = 2, of multiplicity 2. This means the parabola touches the x-axis only once.

So, the x-intercept of f(x) = x2 - 4x + 4 is (2, 0).

Example 2

Find the y- and x-intercepts of the function: f(x) = x2 + 9

Solution

The y-intercept is the point where x = 0. It is the point (0, C). For the given function, it is (0, 9).

To find the x-intercepts, replace f(x) with 0 and then solve for x.

 Original function. Substitute 0 for f(x). f(x) = x2 + 9 0 = x2 + 9

To solve for x:

 Subtract 9 from both sides. -9 = x2 Take the square root of each side. = x Simplify. Â±3i = x

Since the solution is two imaginary roots, the function f(x) = x2 + 9 has no x-intercepts. That is, it does not cross the x-axis.

Note:

Remember, when you take the square root of each side of an equation you must include both the positive and negative square roots. That is why we need the Â± in =  x.

Remember, taking the square root of a negative number results in an imaginary number, which we indicate with the letter i.

 All Right Reserved. Copyright 2005-2024