Question

Question #c26b5

Answer 1

The equation of parabola is `y= 3(x-1)^2 -48`

Explanation:

Lowest point is vertex of the parabola. y-coordinate of vertex is `-48`.

x-coordinate of vertex is mid point of x-intercepts `-3 and 5` i.e `1`. So vertex is at `(1,-48)`

The equation of parabola is `y=a(x-h)^2+k or y=a(x-1)^2 -48`.

The point `(5,0)` is on the parabola , so the point will satisfy the equation. `0= a(5-1)^2 -48 or 0 = 16a-48 or 16a=48 or a=3`

Hence the equation of parabola is `y= 3(x-1)^2 -48`.
graph{3(x-1)^2 -48 [-160, 160, -80, 80]} [Ans]