Question

Rewrite the function by completing the square F(x)=2x^2+13x+20

Answer 1

Answer:

the correct answer is: f(x)=2(x+13/4)²+-9/8. i hope it help

Answer 2

Answer:

$F(x)=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}.$

Step-by-step explanation:

Consider the function $F(x)=2x^2+13x+20.$

Rewrite it as follows:

$F(x)=(2x^2+13x)+20=2\left(x^2+\dfrac{13}{2}x\right)+20=2\left(x^2+\dfrac{13}{2}x+\left(\dfrac{13}{4}\right)^2-\left(\dfrac{13}{4}\right)^2\right)+20=2\left(x^2+\dfrac{13}{2}x+\dfrac{169}{16}\right)-2\cdot \dfrac{169}{16}+20.$

Since

$x^2+\dfrac{13}{2}x+\dfrac{169}{16}=\left(x+\dfrac{13}{4}\right)^2,$

you get

$F(x)=2\left(x+\dfrac{13}{4}\right)^2+20-\dfrac{169}{8}=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}.$