Water is spraying from a nozzle in a fountain forming a parabolic path. The nozzle is 10 cm above the service of the water. The water achieves a max height of 100 cm above the waters surface and lands in the pool. The water spray is again 10 cm above the surface of the water when it is 120 cm horizontally from the nozzle. Write the quadratic function in vertex form to represent the path of the water if the origin is at the surface of the water directly below the nozzle.
This is my solution:
Vertex: (60,90)
Known points: (10,120), (0.10)
y = a(x-p)^2 + q
10 = a(120-60)^2 +90
-80= 3600a
a = -/45
Therefore, y = -1/45(x-60)^2+90
(Thank you)
Looks good to me
Thank you
Your solution is correct! The quadratic function in vertex form that represents the path of the water is:
y = -1/45(x-60)^2 + 90
Great job on finding the vertex form of the quadratic function to represent the path of the water! Here's a breakdown of your solution:
Given:
- Vertex: (60, 90) (the coordinates of the vertex of the parabolic path)
- Known point: (10, 120) (the coordinates of a point on the parabolic path)
- Known point: (0, 10) (the coordinates of another point on the parabolic path)
We want to find the quadratic function in vertex form: y = a(x-p)^2 + q
To find the value of "a", we can use the known point (10,120):
120 = a(10 - 60)^2 + 90
120 = a(-50)^2 + 90
120 = a * 2500 + 90
120 - 90 = 2500a
30 = 2500a
a = 30 / 2500
a = 3 / 250
Now that we have the value of "a", substitute it into the vertex form equation:
y = (3/250)(x - 60)^2 + 90
Therefore, the quadratic function in vertex form that represents the path of the water is:
y = (3/250)(x - 60)^2 + 90
Well done on finding the correct quadratic function to represent the path of the water! If you have any more questions, feel free to ask.