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 statements that are true are:

A. The scenario can be represented by the function h(x) = –0.25(x)(x – 5).

E. The scenario can be represented by the function h(x) = –1(x – 5).

which statements are true?

Given that the curve produced by the water from the hose has zeros at 0 and 5 and passes through the point (4, 1), determine which statements are true.

A. The scenario can be represented by the function h(x) = –0.25(x)(x – 5).

To check if this statement is true,  substitute the given point (4, 1) into the equation:

h(4) = –0.25(4)(4 – 5) = –0.25(4)(-1) = 0.25(4)(1) = 1

Since h(4) evaluates to 1, which matches the y-coordinate of the given point, this statement is true.

B. The scenario can be represented by the function h(x) = (x)(x + 5).

This statement does not match the given information since the function does not account for the zeros at 0 and 5. Therefore, this statement is false.

C. The vertex is on the line x = 2.5.

Since the vertex is not mentioned or indicated by the given information, we cannot determine its exact location. Therefore, this statement is undetermined.

D. The greatest height that the water reaches is 1.5 units.

Since the given point (4, 1) lies on the curve, and no other information suggests a greater height, we cannot conclude that the greatest height reached is 1.5 units. Therefore, this statement is false.

E. The scenario can be represented by the function h(x) = –1(x – 5).

To check if this statement is true, let's substitute the given point (4, 1) into the equation:

h(4) = –1(4 – 5) = –1(-1) = 1

Since h(4) evaluates to 1, which matches the y-coordinate of the given point, this statement is true.

In summary, the statements that are true are:

A. The scenario can be represented by the function h(x) = –0.25(x)(x – 5).

E. The scenario can be represented by the function h(x) = –1(x – 5).

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Answer:A and C

Step-by-step explanation:

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