Hello,
[tex]h(x) = 2x^2+11x+15[/tex]
we can notice that
[tex](x+\dfrac{11}{4})^2 = x^2+\dfrac{11}{2}x+{(\dfrac{11}{4})}^2[/tex]
so we can write
[tex]2x^2+11x = 2 [ {(x+\dfrac{11}{4})^2-{(\dfrac{11}{4})}^2 ][/tex]
then it comes
[tex]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}}[/tex]so
[tex]h(x) = 2{(x+\dfrac{11}{4})^2-{\dfrac{1}{8}}[/tex]
