Convert a quadratic function from the general form to the vertex form

We show you in this lesson two ways to convert a quadratic function from the general form to the vertex form. 

How to convert a quadratic function from the general form to the vertex form by completing the square.

Write the function f(x) = 3x2 - 12x + 10 in vertex form by completing the square

f(x) = 3x2 - 12x + 10

First, group the quadratic term and the linear term.

f(x) = (3x2 - 12x) + 10

Since we need a leading coefficient of 1 to complete the square, factor out the 3.

f(x) = 3(x2 - 4x) + 10

Complete the square. Review this lesson about completing the square if needed.
Basically, you need to find the constant term for x2 - 4x.

The constant term is (-4/2)2 = (-2)2 

Add (-2)to 3(x2 - 4x) + 10. The way we are going to do that is by adding (-2)and then removing (-2) so we do not change the function.

f(x) = 3(x2 - 4x + (-2)2 - (-2)2) + 10

f(x) = 3(x2 - 4x + (-2)2 - 4) + 10

f(x) = 3(x2 - 4x + (-2)2)+ 3(- 4) + 10

f(x) = 3(x2 - 4x + (-2)2) + -12 + 10

f(x) = 3(x - 2)2 + -2

The vertex form is f(x) = 3(x - 2)2 + -2

How to convert a quadratic function from the general form to the vertex form by using the formula to find the x-coordinate of the vertex: x = -b/2a

Write the function f(x) = 3x2 - 12x + 10 in vertex form using the formula to find the x-coordinate of the vertex.

f(x) = 3x2 - 12x + 10

Find the x-coordinate of the vertex using x = -b/2a

a = 3, b = -12 and c = 10

x = - -12/2(3) = 12/6 = 2

Find the y-coordinate of the vertex using f(x) = 3x2 - 12x + 10

f(2) = 3(2)2 - 12(2) + 10

f(2) = 3(4) - 24 + 10

f(2) = 12 - 24 + 10

f(2) = -12 + 10

f(2) = -2

The vertex form of a quadratic function is f(x) = a(x - h)2 + k, where a, h, and k are real numbers and (h,k) is the vertex.

Therefore, a  = 3, h = 2 and k  = -2

f(x) = 3(x - 2)2 + -2

Recent Articles

  1. Box and Whiskers Plot

    Nov 18, 22 08:20 AM

    Easily learn to construct a box and whiskers plot for a set of data by using the median and the extreme values.

    Read More

  2. Binary Number System

    Nov 17, 22 10:53 AM

    This lesson will give you a deep and solid introduction to the binary number system.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes