Question

How do you write `f(x) = x^2+7x+10` in vertex form?

Answer 1

`y=(x+7/2)^2-9/4`

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 constant.

`"for a parabola in standard form "y=ax^2+bx+c`

`x_(color(red)"vertex")=-b/(2a)`

`y=x^2+7x+10" is in standard form"`

`"with "a=1,b=7,c=10`

`rArrx_(color(red)"vertex")=-7/2`

`"substitute this value into f(x) for y-coordinate"`

`y_(color(red)"vertex")=(-7/2)^2+(7xx-7/2)+10=-9/4`

`rArrcolor(magenta)"vertex "=(-7/2,-9/4)`

`rArry=(x+7/2)^2-9/4larrcolor(red)" in vertex form"`