Question

What is the equation of the parabola with vertex `(-5,-2)` and that passes through `(-4,0)`?

Answer 1

The equation of parabola is `y =2(x+5)^2-2`

Explanation:

The vertex form of equation of parabola is

`y = a(x-h)^2+k ; (h,k)` being vertex , here `h=-5 , k= -2`

So the equation of parabola is `y = a(x+5)^2-2 ;`. The parabola

passes through point `(-4,0)`, the point will satisfy the equation

of parabola. Putting `x=-4 and y=0` in the equation we get,

`0=a(-4+5)^2-2 or 0= a-2 or a= 2`

Hence ,the equation of parabola is `y =2(x+5)^2-2`

graph{2(x+5)^2-2 [-10, 10, -5, 5]}