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

Answer:

$\boxed{ \ 2(x+\dfrac{3}{4})^2-\dfrac{25}{8}\ }$

Step-by-step 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

    $2(x+\dfrac{3}{4})^2$

indeed

   $2(x+\dfrac{3}{4})^2=2x^2+3x+2(\dfrac{3}{4})^2=2x^2+3x+\dfrac{9}{8}$

so we can write that

   $2x^2+3x=2(x+\dfrac{3}{4})^2-\dfrac{9}{8}$

then

   $2x^2+3x-2=2(x+\dfrac{3}{4})^2-\dfrac{9}{8}-2=2(x+\dfrac{3}{4})^2-\dfrac{9+16}{8}=2(x+\dfrac{3}{4})^2-\dfrac{25}{8}$