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Water Fountain Parabola
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Transcript
Water Fountain Parabola
Step 1: Take a picture of a water fountain
Step 2: Mark 3 points on the path of the water
Step 3: Create a parabola
Step 4: Find your equation
Vertex Form: y=a(x-h)^2+k
Equation: y=a(x+5)^2+14
Vertex: (-5,14)
Second Point: (-8,13)
13=a(-8+5)^2+14
13=a(-3)^2+14
13=9a+14
-1=9a
-1/9=a
Final Equation: y=-1/9(x+5)^2+14
I chose this quadratic form because I already had the vertex figured out, so it was much less difficult to find out the equation this way.
I could have chosen the intercept form equation, because I would have easily been able to find the intercepts, but I already had the vertex figured out.
The highest point on the path of water was the vertex, because the water does not exceed that point.
If there was no catch basin, the water would hit the ground at approximately 81 centimeters under the fountain.
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