Answer:
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 [tex]h(x)=-x^2+5x[/tex]
[tex]x=-\dfrac{b}{2a}[/tex]
x-coordinate of vertex of h(x)
[tex]x=-\dfrac{-5}{2}=2.5[/tex]
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.
