Question

What is the equation of the parabola that has a vertex at `(-12, -11)` and passes through point `(-9,16)`?

Answer 1

`y=3x^2+72x+421`

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"`

`"here "(h,k)=(-12,-11)`

`y=a(x+12)^2-11`

`"to find a substitute "(-9,16)" into the equation"`

`16=9a-11rArr9a=27rArra=3`

`y=3(x+12)^2-11larrcolor(red)"in vertex form"`

`"distribute and rearrange"`

`y=3(x^2+24x+144)-11`

`color(white)(y)=3x^2+72x+421larrcolor(red)"in standard form"`