The trajectory of the water from Fountain A is represented by a function in standard form while the trajectory of the water from Fountain B is represented by table of values. Compare the vertex of each function. Which trajectory reached greatest height in feet?

The correct answer is: B reached greatest height.

We have given two fountains A and B
For fountain A trajectory
f(x) = -x² + 2x + 8
x = -2 / 2(-1)
= -2 / -2
x = 1
The x coordinate of the vertex is the same:
h = 1
The y coordinate of the vertex is :
k = f(h)
k = -(h)² + 2(h) + 8
k = -(1)² + 2(1) + 8
k = -1 + 2 + 8
k = 9
Therefore, the vertex is (1 , 9)
For fountain B trajectory
Height of the fountain can be measured by y coordinate of the trajectory
So, maximum y coordinate of fountain B is 10 in the given values
And the y coordinate of vertex of fountain A is 9
So y- coordinate of fountain B is more than of fountain A
Therefore , Fountain B reached greatest height.