Question

Rewrite the function by completing the square. h(x)=2x^2+11x+15


h(x)=__(x+__)^2+__

Answer 1

h(x)+2(x+11/4)^2+-1/8

Explanation:

Answer 2

Hello,

`h(x) = 2x^2+11x+15`

we can notice that

`(x+(11)/(4))^2 = x^2+(11)/(2)x+{((11)/(4))}^2`

so we can write

`2x^2+11x = 2 [ {(x+(11)/(4))^2-{((11)/(4))}^2 ]`

then it comes

`h(x) = 2 [ {(x+(11)/(4))^2-{((11)/(4))}^2 ] + 15\\= 2 {(x+(11)/(4))^2 +15-{(11^2)/(8)}\\= 2 {(x+(11)/(4))^2 +{(15*8-11^2)/(8)}`so

`h(x) = 2{(x+(11)/(4))^2-{(1)/(8)}`