Question

Rewrite the function by completing the square F(x)=2x^2+3x-2

Answer 1

y = 2 ( x + 3/4 )^2 − 25 8

Answer 2

`\boxed{ \ 2(x+(3)/(4))^2-(25)/(8)\ }`

Explanation:

we should write this function

`2x^2+3x-2`

this way
`a(x-b)^2+c`

let s check the first terms in
`x^2` and x

`2x^2+3x`

this is the beginning of

`2(x+(3)/(4))^2`

indeed

`2(x+(3)/(4))^2=2x^2+3x+2((3)/(4))^2=2x^2+3x+(9)/(8)`

so we can write that

`2x^2+3x=2(x+(3)/(4))^2-(9)/(8)`

then

`2x^2+3x-2=2(x+(3)/(4))^2-(9)/(8)-2=2(x+(3)/(4))^2-(9+16)/(8)=2(x+(3)/(4))^2-(25)/(8)`