What is the maximum height the diver is above the water?

Question

The path of a cliff diver as he dives into a lake,is given by the equation y=-(x-10)^2+75, where y meters is the divers height above the water and x meters is the horizontal distance travelled by the diver.

Answer 1

y=a(x-h)^2+k  is called vertex form of a quadratic function.  When a quadratic function is written in vertex form, we can easily determine the vertex (h, k). If the coefficient a > 0, then the parabola opens upward and the vertex is the lowest point on the parabola. We say that k is the minimum value of the quadratic function. On the other hand, if the coefficient a < 0, then the parabola opens downward and the vertex is the highest point on the parabola. In this case, k is the maximum value of the quadratic function

y=-(x-10)^2+75

(h,k)=(10,75)

Maximum height of  the diver  above  water is 75m.