QF - Convert Between Forms (Lesson)

Convert Between Forms

Given a quadratic function in vertex form, let's convert it to standard form:

$f(x)=-2(x-1)^2+7$                          Expand the binomial squared

$f(x) = -2(x - 1)(x - 1) + 7$     

     

Then, start with the exponent and FOIL the $(x-1)^2$:

$f(x)=-2(x^2-x-x+1)+7$          Combine like terms

$f(x)=-2(x^2-2x+1)+7$

 

Then, distribute the 2:

$f(x)=-2x^2+4x-2+7$                   Combine like terms

$f(x)=-2x^2+4x+5$

 

Converting from standard form to vertex form requires us to utilize the completing the square method we learned in a previous lesson. Watch this video to learn how to do that.

 

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Convert from Standard Form to Vertex Form Practice

Try these problems.

1. f(x) = 2x² + 8x + 3
2. f(x) = x² + 10x + 2
3. f(x) = -3x² -6x + 4

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

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