Question

What is the equation of the parabola that has a vertex at `(-6, 3)` and passes through point `(12,9)`?

Answer 1

`y=1/3x^2+4x+15`

Explanation:

`"the equation of a parabola in "color(blue)("vertex form"` is.

`•color(white)(x)y=a(x-h)^2+k`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is a multiplier"`

`"here "(h,k)=(-6,3)`

`y=a(x+6)^2+3`

`"to find a substitute "(12,9)" into the equation"`

`9=18a+3`

`18a=9-3=6rArra=6/18=1/3`

`y=1/3(x+6)^2+3larrcolor(red)"in vertex form"`

`"distributing gives"`

`y=1/3(x^2+12x+36)+3`

`y=1/3x^2+4x+15larrcolor(red)"in standard form"`