Question

What is the vertex form of `2y=(3x -3)(x - 5)`?

Answer 1

`y=3/2(x-3)^2+(-6)` with vertex at `(3,-6)`

Explanation:

The vertex form of a parabola is
`color(white)("XXX") y= m(x-a)^2+b`
for a parabola with center at `(a,b)`

`2y=(3x-3)(x-5)`

`rarr 2y=3(x-1)(x-5)`

`rarr 2/3y =x^2-6x+5`

`rarr 2/3y=(x^2-6x+9) +5 (-9)`

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

`rarr y=3/2(x-3)^2 - 3/2xx4`

`rarr y = 3/2(x-3)^2 + (-6)`

graph{((3x-3)(x-5))/2 [-1.27, 9.823, -7.815, -2.266]}