Unit 2 Day 12 Review of Quadratics

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) = -40t2 + 440t – 400 P(t) = -40t2 – 440t – 400 P(t) = -40t2 – 360t + 400 P(t) = -40t2 – 360t – 400 P(t) = 40t2 – 440t + 400

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! 

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) = -40t2 + 440t – 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 – 400 + 40t subtracted polynomials = – 40t2 + (400t + 40t ) –400 combined like terms = – 40t2 + 440t –400 simplified

Homework Answers Packet p. 15 1. 2. 3. x < -4 or x > 5 5. 2 < x < 8 -3 ≤ x ≤ -1 7. z ≤ 0 or z ≥ ¾ -3/2 < t < 3/2 9. -3 ≤ x ≤ -4/9 10. x < -1/2 or x > -1/2 11. All real #s

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

Homework Answers Packet p. 16 12. 13. 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.

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

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

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