1. Unit 2 Day 12
Review of Quadratics

2. Warm Up
13. Each year, a local school’s Rock the Vote committee organizes a public rally. Based on previous years, the organizers decided that the Income from ticket sales, I(t) is related to ticket price t by the equation I(t) = 400t – 40t2. Cost C(t) of operating the public event is also related to ticket price t by the equation C(t) = 400 – 40t.
a. What ticket price(s) would generate the greatest income? What is the greatest income possible? Explain how you obtained the value you got. Ticket price(s) _________ Income _______
For what ticket price(s) would the operating costs be equal to the income from ticket sales? Explain how you obtained the answer.
Which of the following rules would give the predicted profit P(t) as a function of the ticket price?
P(t) = -40t t – 400
P(t) = -40t2 – 440t – 400
P(t) = -40t2 – 360t + 400
P(t) = -40t2 – 360t – 400
P(t) = 40t2 – 440t + 400

3. Warm Up ANSWERS
13. Each year, a local school’s Rock the Vote committee organizes a public rally. Based on previous years, the organizers decided that the Income from ticket sales, I(t) is related to ticket price t by the equation I(t) = 400t – 40t2. Cost C(t) of operating the public event is also related to ticket price t by the equation C(t) = 400 – 40t.
a. What ticket price(s) would generate the greatest income? What is the greatest income possible? Explain how you obtained the value you got. Ticket price(s) _________ Income _______
For what ticket price(s) would the operating costs be equal to the income from ticket sales? Explain how you obtained the answer.
$5 $1000
Enter the income equation I(t) in the calculator and find the maximum OR
Factor to find the zeros then average the zeros to find the vertex x-value. Then substitute that x-value into the I(t) equation to find the y.
For a $10 Ticket, the income and costs are both $0
For a $1 Ticket, the income and costs are both $360.
Set I(t) = C(t) then solve by finding the intersections using our skills from yesterday’s lesson! 

4. Warm Up ANSWERS
Each year, a local school’s Rock the Vote committee organizes a public rally. Based on previous years, the organizers decided that the Income from ticket sales, I(t) is related to ticket price t by the equation I(t) = 400t – 40t2. Cost C(t) of operating the public event is also related to ticket price t by the equation C(t) = 400 – 40t.
c. Which of the following rules would give the predicted profit P(t) as a function of the ticket price?
P(t) = -40t t – 400
P(t) = -40t2 – 440t – 400
P(t) = -40t2 – 360t + 400
P(t) = -40t2 – 360t – 400
P(t) = 40t2 – 440t + 400
Profit = Income – Cost
P(t) = (400t – 40t2 ) – (400 – 40t)
= 400t – 40t2 – t subtracted polynomials
= – 40t2 + (400t + 40t ) – combined like terms
= – 40t t – simplified

5. Homework Answers Packet p. 15
x < -4 or x > < x < 8
-3 ≤ x ≤ z ≤ 0 or z ≥ ¾
-3/2 < t < 3/ ≤ x ≤ -4/9
10. x < -1/2 or x > -1/ All real #s

6. Homework Answers Packet p. 15
Work for Packet p. 15 Top
NEED TO ADD THESE IN!!!

7. Homework Answers Packet p. 16
14a.
14b. (5/2, 30) (-8, 9)
15. It is possible for a system with a linear equation and a quadratic equation to have no solution if their graphs do not intersect, like shown in the diagram.

8. Homework Answers Packet p. 16
Work for Packet p. 16

9. Homework Answers Packet p. 16
Work for Packet p. 16

11. Quadratics Scavenger Hunt
Review!
On notebook paper….
Quadratics Scavenger Hunt
Letter Question Work Solution(s)