How do you solve y=−2x2+4x+7 using the completing square method?

1 Answer
Morgan
Dec 31, 2016

See below.

Explanation:

To complete the square, we take a quadratic equation of the form

ax2+bx+c=0

And turn it into

a(x+d)2+e=0

Begin by factoring out −2 to get a coefficient of 1 for the x2 term.

y=−2(x2−2x−72)

Now look at the coefficient of the x term.

y=−2(x2−2x−72)

Divide this coefficient by 2 and square the result:

(−22)2=(1)2=1

I will rewrite the equation:

y=−2(x2−2x+f−72−f)

Replace f with the result of the above operation:

⇒y=−2(x2−2x+1−72−1)

We separate off the first part of the parentheses from the second:

⇒y=−2[(x2−2x+1)−72−1]

Simplify:

⇒y=−2[(x2−2x+1)−92]

What we have left in the parentheses is a perfect square. Factor:

⇒y=−2[(x−1)2−92]

Distribute −2:

⇒y=−2(x−1)2+9

Or, equivalently:

y=9−2(x−1)2

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