Question

What is the equation of the parabola that has a vertex at `(-1, 6)` and passes through point `(3,22)`?

Answer 1

Equation of the parabola is `y= x^2+2*x+7`

Explanation:

We use here the standard equation of Parabola `y= a (x-h)^2 +k` Where h an k are the co-ordinates of Vertex. Here h = -1 and k=6 (given) So the equation of the Parabola becomes `y = a(x+1)^2+6`. Now the Parabola passes through the point (3,22). So this point will satisfy the Equation. Then `22 = a(3+1)^2+6` or `a*16=22-6 or a=1`
So the Equation of the parabola is `y= 1*(x+1)^2+6 or y= x^2+2*x+7`[Answer] graph{x^2+2x+7 [-80, 80, -40, 40]}