Answer :
We have been given that Ming throws a stone off a bridge into a river below.
The stone's height (in meters above the water), x seconds after Ming threw it, is modeled by [tex]h(x)=-5(x-1)^2+45[/tex].
We are asked to find the maximum that the stone will reach.
We can see that our given equation is in vertex form of parabola [tex]y=a(x-h)^2+k[/tex] with vertex at point (h,k).
We can also see that leading coefficient is negative, so our given parabola is a downward opening parabola and its maximum value be at vertex.
The maximum height will be equal to y-coordinate of vertex.
We can see that vertex of our given parabola is at point (1,45). Therefore, the maximum height will be 45 meters.