Question

What is the vertex form of `y= x^2-x-56`?

Answer 1

`y=(x-1/2)^2-225/4`

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`

`"the x-coordinate of the vertex is "`

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

`y=x^2-x-56" is in standard form"`

`"with " a=1,b=-1,c=-56`

.>`rArrx_(color(red)"vertex")=-(-1)/2=1/2`

`"substitute into function for y-coordinate of vertex"`

`rArry_(color(red)"vertex")=(1/2)^2-1/2-56=-225/4`

`rArrcolor(magenta)"vertex" =(1/2,-225/4)`

`rArry=(x-1/2)^2-225/4larrcolor(red)" in vertex form"`