H(x)=-5(x-1)^2+45
what is the maximum height

9514 1404 393

  45

Step-by-step explanation:

The equation is that of a parabola in vertex form.

  y = a(x -h)^2 +k

where 'a' is the vertical scale factor and (h, k) is the vertex.

Comparing this to the given function, you find ...

  a = -5

  h = 1

  k = 45

The negative value of 'a' tells you the parabola opens downward, so the y-value of the vertex is the maximum value of the function: 45.