Question

What is the vertex form of `7y=(2x -8)(4x - 5)`?

Answer 1

`y=8/7(x-21/8)^2-121/56`

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"`

`"expand the factors"`

`rArr7y=8x^2-42x+40`

`"to express in vertex form use "color(blue)"completing the square"`

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

`rArr7y=8(x^2-21/4+5)`

`• " add/subtract "(1/2"coefficient of x-term")^2" to "`
`x^2-21/4x`

`7y=8(x^2+2(-21/8)xcolor(red)(+441/64)color(red)(-441/64)+5)`

`color(white)(7y)=8(x-21/8)^2+8(-441/64+5)`

`color(white)(7y)=8(x-21/8)^2-121/8`

`rArry=8/7(x-21/8)^2-121/56`