Question

How do you write `y=3x^2-9x` into vertex form?

Answer 1

`y=3(x-3/2)^2-27/4`

Explanation:

`"the equation of a parabola in "color(blue)"vertex form"` is

`•color(white)(x)y=a(x-h)^2+k`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is a multiplier"`

`"to obtain this form use "color(blue)"completing the square"`

`y=3(x^2-3x)`

`color(white)(y)=3(x^2+2(-3/2)x color(red)(+9/4)color(red)(-9/4))`

`color(white)(y)=3(x-3/2)^2-27/4larrcolor(blue)"in vertex form"`