how would i write this function in vertex form? 2x^2 + 7x + 3?

Question

and show steps please

Answer 1

The vertex form is expressed as
(x-h)^2=4p(y-k)

Where the vertex is (h,k)

Multiply out the equation to get
(x^2-2hx+h^2)/4p+k=y

Then solve for the constants

1/(4p)=2
p=1/8
-h/(2p)=7
h=-7/4
h^2/(4p)+k=3
k=-25/8

So
(x+7/4)^2=1/2(y+25/8)

j

Answer 2

2x^2+7x+3=y

2(x^2+7/2x)=y-3

1/2*7/2=7/4 and (7/4)^2=49/16

2(x^2+7/2x+7/4)=y-3+2*49/16

2(x+7/4)^2=y-24/8+49/8

2(x+7/4)^2=y+25/8


vertex @(-7/4,-25/8)