Question

What is the equation of the parabola that has a vertex at `(-15, -4)` and passes through point `(15,5)`?

Answer 1

`y=1/100(x+15)^2-4`

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 constant.

`"here " (h,k)=(-15,-4)`

`rArry=a(x+15)^2-4`

`"to find a use the point that parabola passes through"`

`"using " (15,5)" that is x = 15 and y = 5"`

`rArr5=a(15+15)^2-4`

`rArr900a=9rArra=1/100`

`rArry=1/100(x+15)^2-4larrcolor(red)" in vertex form"`
graph{1/100(x+15)^2-4 [-20, 20, -10, 10]}