Question

What is the vertex form of `y= -5x^2+x-2`?

Answer 1

`y=-5(x-1/10)^2-39/20`

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.

`"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=-5x^2+x-2" is in standard form"`

`"with "a=-5,b=1,c=-2`

`rArrx_(color(red)"vertex")=-1/(-10)=1/10`

`"substitute this value into the equation for y"`

`y_(color(red)"vertex")=-5(1/10)^2+1/10-2=-39/20`

`"here "(h,k)=(1/10,-39/20)" and "a=-5`

`rArry=-5(x-1/10)^2-39/20larrcolor(red)" in vertex form"`