Question

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

Answer 1

`y=2(x+9/4)^2-1/8`

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"`

`y=(x+2)(2x+5)larrcolor(blue)"expand the factors"`

`color(white)(y)=2x^2+9x+10`

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

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

`rArry=2(x^2+9/2x+5)`

`• " add/subtract "(1/2"coefficient of the x-term")^2" to"`
`x^2+9/2x`

`rArry=2(x^2+2(9/4)xcolor(red)(+81/16)color(red)(-81/16)+5)`

`color(white)(y)=2(x+9/4)^2+2(-81/16+5)`

`color(white)(y)=2(x+9/4)^2-1/8larrcolor(red)"in vertex form"`