Question

Convert the equation f(x)=1/2x^2+3x-2 to vertex form

Answer 1

Explanation:

Hello, please consider the following.

The "vertex form" is as below.

`y=a(x-h)^2+k\\\\\text{Where (h, k) is the vertex of the parabola.}\\`

Let's do it!

`f(x)=(1)/(2)x^2+3x-2\\\\f(x)=(1)/(2)\left(x^2+3*2*x\right) -2\\\\f(x)=(1)/(2)\left( (x+3)^2-3^2\right)-2\\\\f(x)=(1)/(2)(x+3)^2-(9)/(2)-(4)/(2)\\\\f(x)=(1)/(2)(x+3)^2-(9+4)/(2)\\\\\large \boxed{\sf \bf \ \ f(x)=(1)/(2)(x+3)^2-(13)/(2) \ \ }`

Thank you.