Question

What is the equation of the parabola that has a vertex at `(2, 3)` and passes through point `(-1,-2)`?

Answer 1

The Equation of the Parabola is `y= a(x-h)^2+3` where (h,k) is the vertex. So `y=a(x-2)^2+3` Now the equation passes through the point (-1,-2) So `-2=a(-1-2)^2+3 or -2 =9*a+3 or 9*a=-5 or a=-5/9`
So the equation of the Parabola becomes `y=-5/9(x^2-4*x+4)+3`
or `y= -5/9*x^2 +20/9*x+7/9` graph{-5/9x^2+20/9x+7/9 [-10, 10, -5, 5]} [Ans]