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Completing the Square

Q: What is completing the square?

A: Completing the square is a technique used to convert from general form, , to standard form, . Why do we need to convert? Standard form is much easier to graph as a parabola.

Let’s look at some examples:

Write each function in the form

a)

. . . → Read More: Completing the Square

Completing the Square when a doesn’t equal 1

b) Convert to standard form by completing the square:

Step 1: In this case, a=2, so we need to do something different: factor out the 2, but only for the x terms:

Now take half of the b term (in this case, b=2) and square it.

Step 2: Important: Add that . . . → Read More: Completing the Square when a doesn’t equal 1

Completing the square when a is negative

c)Convert to standard form by completing the square:

Step 1: In this case, a=-2, so factor out the -2 term, but only for the x terms:

Now take half of the b term (in this case, b=(3/2)) and square it.

Step 2: Important: Add that number to the equation inside the . . . → Read More: Completing the square when a is negative