MATH HONORS 2: UNIT 2 EXTRA REVIEW – Quadratics
1. Nottingham Castle below is a daunting castle to attack. It has enormous 50 meter high walls that are 10
meters thick. There are archers on the castle walls firing arrows to stop your attempt to rescue Maid
Marion. You must therefore be no closer to the castle than 100 meters. Your target is the Sheriff of
Nottingham. He is in his parlor 20 meters inside the walls of the castle, sitting 10 meters above the
ground
Using any suitable strategy (including technology), find an equation that models a reasonable flight
path of a successful projectile catapulted over the castle walls—the aim is to hit the sheriff!
2. A lemonade stand sells cups of lemonade for $0.50 each, and is able to sell 120 cups of lemonade each
day. A marketing study discovers that for each 5-cent increase to the price of a cup of lemonade, the
lemonade stand will only lose 6 customers.
(a) How much money will the lemonade stand make in one day if it sells cups of lemonade for $0.60
each?
(b) Write an expression that represents the amount of money that the lemonade stand will make in
one day if it increases the price of each cup of lemonade by “x” 5-cent increments?
(c) Find the price of each cup of lemonade that will maximize the amount of money made in a day.
(d) What is the maximum amount of money that the lemonade stand can make in a day?
(e) Write a quadratic function “M(x)” for the money made by the lemonade stand in a day if it
increases the price of each cup of lemonade by “x” 5-cent increments:
i.
in standard form
ii.
in vertex form
3. Without using a calculator, express f(x) = -0.25x2 + 3x + 2 in vertex form.
4. Find a quadratic inequality in two variables that describes the shaded region given below:
5. Given that x1 
2  3i
and x2 are the solutions to the quadratic function f  x   0 , find x1  x2 .
3i
6. Solve the quadratic inequality x 4  3x 2  4  0 .
2
7. Given that g  x   kx  5x  4k has two real solutions, find k .