The curve produced by the water coming from a hose is sketched onto a graph with zeros at 0 and 5. the point (4, 1) also lies on the curve. if h(x) represents the vertical distance from where the water first comes out of the hose and x represents the horizontal distance, which statements are true? check all that apply.
a. the scenario can be represented by the function h(x) = –0.25(x)(x – 5).
b. the scenario can be represented by the function h(x) = (x)(x + 5).
c. the vertex is on the line x = 2.5.
d. the greatest height that the water reaches is 1.5 units.
e. the scenario can be represented by the function h(x) = –1(x – 5).

The vertex is on the line x = 2.5

C is correct.

Step-by-step explanation:

The curve produced by the water coming from a hose is sketched onto a graph with zeros at 0 and 5. The point (4, 1) also lies on the curve.

If h(x) represents the vertical distance from where the water first comes out of the hose and x represents the horizontal distance

h(x) curve must be parabolic because flow of water is parabolic path.

It is two degree polynomial. Possible zeros are 0 and 5

h(x)=a(x-0)(x-5)

The point (1,4) also lies on the curve.

h(1)=4

4=a(1-5)

a=-1

Thus, The equation of path is h(x)=-x(x-5)

Vertex of

x-coordinate of vertex of h(x)

Axis of parabola: x=2.5

At x=2.5

h(2.5)=6.25

Vertex: (2.5,6.25)

The greatest value of curve is y-value of vertex.

Thus, The greatest height of water reaches is 6.25 units.

Now, we check possible option correct.

For graph please find attachment.

C is correct.