Question

What is the vertex form of `y= (x -1)(x/2 + 2)`?

Answer 1

`y=1/2(x+3/2)^2-25/8`

Explanation:

`"expand the factors using FOIL"`

`y=1/2x^2+3/2x-2`

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

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

`"factor out "1/2`

`y=1/2(x^2+3x-4)`

`• " add/subtract "(1/2"coefficient of the x-term")^2" to"`
`x^2+3x`

`y=1/2(x^2+2(3/2)x color(red)(+9/4)color(red)(-9/4)-4)`

`color(white)(y)=1/2(x+3/2)^2+1/2(-9/4-4)`

`color(white)(y)=1/2(x+3/2)^2-25/8larrcolor(red)"in vertex form"`