1. Module Dorton Arena
5/17/18

2. Dorton Arena at the State Fairgrounds in Raleigh, North Carolina, has the shape of two intersecting parabolas. An aerial model of Dorton Arena has been created and put on a set of axes. The shape of one of the parabolas can be modeled by the equation 𝑓 𝑥 = 𝑥 2 −127𝑥, where 𝑥 and 𝑓(𝑥) are measured in feet.

3. The parabola that is open up because the a value is positive.
1. Which parabola is modeled by this equation? How do you know?   
The parabola that is open up because the a value is positive.

4. Domain: (−∞,∞) Range: −𝟒𝟎𝟑𝟐.𝟐𝟓, ∞ X-intercepts: (0, 0) & (127, 0)
2. What are the features of the parabola modeled by the equation 𝑓 𝑥 = 𝑥 2 −127𝑥? Include domain, range, intercepts, maxima or minima, intervals of increase and decrease.
Domain: (−∞,∞)
Range: −𝟒𝟎𝟑𝟐.𝟐𝟓, ∞
X-intercepts: (0, 0) & (127, 0)
Y-intercept: (0, 0)
Vertex/Minimum: (63.5, − )
Increasing: (𝟔𝟑.𝟓, ∞)
Decreasing: (−∞, 𝟔𝟑.𝟓)

5. Yes, the parabola matches and the table matches
3. Can the other parabola be modeled by the equation 𝑓(𝑥)=−𝑥(𝑥−127)? How do you know?
Yes, the parabola matches and the table matches
𝒇 𝒙 =− 𝒙 𝟐 +𝟏𝟐𝟕𝒙

6. Domain: (−∞,∞) Range: (−∞, 𝟒𝟎𝟑𝟐.𝟐𝟓] X-intercepts: (0, 0) & (127, 0)
4. What are the features of the parabola modeled by the equation 𝑓 𝑥 = −𝑥 𝑥? Include domain, range, intercepts, maximums or minimums, intervals of increase and decrease.
Domain: (−∞,∞)
Range: (−∞, 𝟒𝟎𝟑𝟐.𝟐𝟓]
X-intercepts: (0, 0) & (127, 0)
Y-intercept: (0, 0)
Vertex/Maximum: (63.5, )
Increasing: (−∞, 𝟔𝟑.𝟓)
Decreasing: (𝟔𝟑.𝟓, ∞)

7. It is 8064.5 feet long It is 127 feet wide
5. Based on these features, how long is Dorton Arena? How wide is the arena?
It is feet long
It is 127 feet wide

8. The slopes are opposites since the equations are opposites
6. Find the average rate of change for each of the parabolas on the interval (20, 40).
7. Will the average rate of change of two parabolas always be the same given the same interval? Explain. X Y 20
2140 40
3480
The open down
parabola has a slope of 67
The open up
parabola has a slope of −67 X Y 20
-2140 40
-3480
The slopes are opposites since the equations are opposites

9. Standard form helps you find the y-intercept (c value)
8. How do the different forms (standard and factored form) help you find different features of the graph?
Standard form helps you find the y-intercept (c value)
Factored form helps you find the x-intercepts which help you find the axis of symmetry