Fountain of Knowledge

By Abbie Hough & Justin Rath

Equations

Vertex Form: y=-9/100(x+11)^2+18

Standard Form: y= -9/100x^2-1.98x+7.11


Questions

What does the height of the water leaving the spout represent?

-It represents the y-intercept of the graph.


At the spot where the water hits the tray, what is the relevance to the equation?

- The spot where it hits the tray is the x-intercept of the graph and it is also the solution to the equation.


What is the maximum height of the water?

- The maximum height of the water was 18 cm.


How far away from the spout is the water when it reaches this maximum height?

- It is 11 cm away from the spout when it reaches maximum height.


What is the domain related to the distance the water is from the spout?

-The domain is [-25,0] which represents the maximum distance that the water traveled from the spout which was 25 cm.


What is the range related to the height of the water?

-The range is [0,18] where 18 represents the maximum height that the water reached.


What 3 points were used to find the regression equations?

- The 3 points were (-11, 18) (0, 5) (-2, 9) which were the vertex, y-intercept, and random points respectively.


What is the regression equation in standard form as well as in vertex form?

- The vertex form is y=-9/100(x+11)^2+18 and the standard form is y= -9/100x^2-1.98x+7.11.