Suppose you toss a volleyball to a friend who is 12 ft away. Midway between you and your friend is a volleyball net, the top of which is 7 ft high. The ceiling of the gymnasium is 25 ft high. When you toss the ball to your friend, the shape of its path forms a parabola. The volleyball is 4 ft off the floor when it leaves your hands, and your friend catches the volleyball 4 ft off the floor as well. Write the equation that models the path of the volleyball if it passes midway between the net and the ceiling. Assume the origin is at the base of the volleyball net. Include the vertex, focus, and directrix of the parabola.

Step-by-step explanation:

Halfway between 7ft and 25ft is (7 + 25)/2 = 16ft.

The vertex is (0, 16).

Two other points on the parabola are (-6, 4) and (6, 4).  Since we have the vertex, we only one of these to find the parabola's equation.

y = a(x - h)^2 + k

y = a(x - 0)^2 + 16 for some a.

y = ax^2 + 16 for some a.

Substitute (-6, 4) or (6, 4) for (x, y) and solve for a.

4 = a(6^2) + 16

-12 = 36a

a = -1/3

y = -x^2/3 + 16

You should be able to take it from here.

Step-by-step explanation:

s + (a + 178) = 2000

step-by-step explanation:

2000 - 178 = 1822

1822 / 2 = 911

911 + 178 = 1089

1089 + 911 = 2000

abha = 1089

shane = 911

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square