Question

How do you write `y =x^2 - 5x - 6` in vertex form?

Answer 1

`y=(x-5/2)^2-49/4`

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^2-5x-6" is in standard form"`

`"with "a=1,b=-5,c=-6`

`rArrx_(color(red)"vertex")=-(-5)/2=5/2`

`"substitute this into the equation for y-coordinate"`

`rArry_(color(red)"vertex")=(5/2)^2-5(5/2)-6=-49/4`

`rArrcolor(magenta)"vertex "=(5/2,-49/4)`

`rArry=(x-5/2)^2-49/4larrcolor(red)" in vertex form"`