For my project I have chosen to measure the parabola made by the nearest water fountain to room 226


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It looks so exciting.
It looks so exciting.




This is my graph. The y intercept is where the water comes out of the fountain.
The point where the water hits the fountain is the x intercept.
The axis of symmetry is x=2.5
The parabola opens down

Vetex
It is a maximum, and a positive number. It is the highest point the water goes, because all other points are lower. I could find it by using the Quadratic Formula.

X-Intercepts
The parabola the water of the fountain forms has two x-intercepts. This is because the water crosses the x-axis twice. The x-intercepts are 9 and -3.75 I found the one on the right by measuring the water fountain and I found the left one by graphing the equation. The intercept on the left does not mean anything, but the one on the right is the point where the water hits the fountain.

Y-Intercepts
The y-intercept is 8.5. I found it by measuring the water fountain. It is the point where the water comes out of the fountain.
The vertex is (2.5, 10.25)

Standard Form
y=-.2496x^2+1.3023x+8.5

Vertex Form
y-8.5=.2496x^2+1.3023x
y+.423996323=(x+.65115)^2

Factored Form
y= -(0.4996x-4.49688)(0.4996x+1.8902)

Question
If the parabola were to continue past the bottom of the fountain, when would it hit the ground? Assume the bottom of the fountain is 4 feet from the ground.

Solution
I can substitute -48 for y

-48= -.2496x^2+1.3023x+8.5

Then, I can do this

0 = -.2496x^2+1.3023x+8.5+48

And then use the quadratic formula.

-1.3023+/- sqrt(1.3023^2-4*-.2496*56.5
2*.2496

The water will hit the ground when it is 17.8786097 inches from the fountain entrance.
More about calculator.
Discriminant
58.1055853


It is not factorable over the integers. It is an irrational number that has been rounded. It is positive.

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