Question

What is the vertex form of `y= 1/2x^2 + 3/2x -4`?

Answer 1

`"The vertex form is : "y=1/2(x+3/2)^2-41/8`

Explanation:

`"The vertex form is formed as y="a(x-h)^2+k`

`"Where (h,k) is vertex coordinates"`

`"we should rearrange the given equation."`

`y=1/2x^2+3/2x-4`

`y=1/2x^2+3/2xcolor(red)(+9/8-9/8)-4`

`y=1/2(color(green)(x^2+3x+9/4))-9/8-4`

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

`y=1/2(x+3/2)^2-41/8`