Question

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

Answer 1

`y=2/3(x-9/4)^2-3/8`

Explanation:

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))`

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

`"to express "3y=(2x-3)(x-3)" in this form"`

`rArr3y=2x^2-9x+9`

`• " the coefficient of the "x^2" term must be 1"`

`rArr3y=2(x^2-9/2x+9/2)`

`• " add/subtract "(1/2"coefficient of x-term")^2`

`"to "x^2-9/2x`

`3y=2(x^2+2(-9/4)xcolor(red)(+81/16)color(red)(-81/16)+9/2)`

`color(white)(3y)=2(x-9/4)^2-9/8larrcolor(blue)"divide by 3"`

`rArry=2/3(x-9/4)^2-3/8larrcolor(red)"in vertex form"`