# 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

## Graph of the Fountain of KnowledgeBoxes are 2cm by 2cm Vertex: (-11, 18) X-Intercept: (-25, 0) y-intercept: (0, 7) Other Point: (-2, 9) Reflection of Other Point: (-20, 9) Axis of Symmetry: x=-11 | ## Graph of the Fountain on the CalculatorX-Intercept (Where the water meets the tray): (-25, 0) | ## The Fountain of KnowledgeThis is the picture of The Fountain of Knowledge located at Tom Thumb. |

## Graph of the Fountain of Knowledge

Boxes are 2cm by 2cm Vertex: (-11, 18) X-Intercept: (-25, 0) y-intercept: (0, 7) Other Point: (-2, 9) Reflection of Other Point: (-20, 9) Axis of Symmetry: x=-11

## Questions

**What does the height of the water leaving the spout represen**t?

-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.**

## Abbie and Justin

11/13/12