Question

What is the equation of the parabola that has a vertex at `(-4, 2)` and passes through point `(-8,-34)`?

Answer 1

`y=-9/4x^2-18x-34`

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)=(-4,2)`

`y=a(x+4)^2+2`

`"to find a substitute "(-8,-34)" into the equation"`

`-34=16a+2`

`16a=-36rArra=(-36)/16=-9/4`

`y=-9/4(x+4)^2+2larrcolor(red)"in vertex form"`

`"expanding and rearranging gives"`

`y=-9/4(x^2+8x+16)+2`

`y=-9/4x^2-18x-34larrcolor(red)"in standard form"`