How do you solve y=-2x^2+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

ax^2+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 x^2 term.

y=-2(x^2-2x-7/2)

Now look at the coefficient of the x term.

y=-2(x^2color(blue)(-2)x-7/2)

Divide this coefficient by 2 and square the result:

(-2/2)^2=(1)^2=1

I will rewrite the equation:

y=-2(x^2-2x+f-7/2-f)

Replace f with the result of the above operation:

=>y=-2(x^2-2x+1-7/2-1)

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

=>y=-2[(x^2-2x+1)-7/2-1]

Simplify:

=>y=-2[(x^2-2x+1)-9/2]

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

=>y=-2[(x-1)^2-9/2]

Distribute -2:

=>y=-2(x-1)^2+9

Or, equivalently:

y=9-2(x-1)^2

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