Question

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

Answer 1

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

Answer 2

`F(x)=2\left(x+(13)/(4)\right)^2-(9)/(8).`

Explanation:

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

Rewrite it as follows:

`F(x)=(2x^2+13x)+20=2\left(x^2+(13)/(2)x\right)+20=2\left(x^2+(13)/(2)x+\left((13)/(4)\right)^2-\left((13)/(4)\right)^2\right)+20=2\left(x^2+(13)/(2)x+(169)/(16)\right)-2\cdot (169)/(16)+20.`

Since

`x^2+(13)/(2)x+(169)/(16)=\left(x+(13)/(4)\right)^2,`

you get

`F(x)=2\left(x+(13)/(4)\right)^2+20-(169)/(8)=2\left(x+(13)/(4)\right)^2-(9)/(8).`