Question

Rewrite the equation f (x) =2x^2 +12x+7 to the form f (x) =a (x-h)^2+k

Answer 1

Complete theh square

isolate x terms
factor out coefient of x^2 term
take 1/2 of 1st degree coefient and square it, add positive and negative inside parnthasees, expand


f(x)=(2x^2+12x)+7
f(x)=2(x^2+6x)+7
6/2=3, 3^2=9
f(x)=2(x^2+6x+9-9)+7
f(x)=2((x+3)^2-9)+7
f(x)=2(x+3)^2-19+7
f(x)=2(x+3)^2-12

Answer 2

You do have to complete the square on part of the problem. Follow my steps in the picture. If you graph the original problem and the answer you should get the same graph. I checked my answer.