Question

What is the equation of the parabola that has a vertex at `(-2, -1)` and passes through point `(1,26)`?

Answer 1

`y=3x^2+12x+11`

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)=(-2,-1)`

`y=a(x+2)^2-1`

`"to find a substitute "(1,26)" into the equation"`

`26=9a-1`

`9a=27rArra=3`

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

`"distributing and simplifying gives"`

`y=3x^2+12x+11larrcolor(red)"in standard form"`
graph{3x^2+12x+11 [-10, 10, -5, 5]}