Question

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


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

Answer 1

Hello,

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

we can notice that

$(x+\dfrac{11}{4})^2 = x^2+\dfrac{11}{2}x+{(\dfrac{11}{4})}^2$

so we can write

$2x^2+11x = 2 [ {(x+\dfrac{11}{4})^2-{(\dfrac{11}{4})}^2 ]$

then it comes

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

$h(x) = 2{(x+\dfrac{11}{4})^2-{\dfrac{1}{8}}$