Quadratic Functions

Vertex

100

Find the vertex of: f(x) = -2x^2

0

200

Find the vertex of: f(x) = x^2 - 3x - 10

1.5

300

Find the vertex of: f(x) = -2x^2 + 3x + 9

0.75

400

Find the vertex of: f(x) = 2x^2 - 16x - 42

4

500

Find the vertex: f(x) = 2x^2 -8x + 5

2

Find the Roots

100

Find the roots of: x^2 - 6x + 4 = 0

No real solution

200

Find the roots of: x^2 = 5x

0, 5

300

Find the roots of: 9 - x^2 = 12

No real solution

400

Find the roots of: 5x^2 + 10x - 4 = -6

Between -2 and -1, between -1 and 0

500

Find the roots of: x^2 - 20 = 2 + x

Between -5 and -4, between 5 and 6

Maximum/Minimum

100

Determine whether this function has a maximum or minimum value, and find that value: f(x) = -x^2 - 12

Max = -12

200

Determine whether this function has a maximum or minimum value, and find that value: f(x) = -x^2 - 7x + 1

Max = 13.25

300

Determine whether this function has a maximum or minimum value, and find that value: f(x) = x^2 + 12x + 27

Min = -9

400

Determine whether this function has a maximum or minimum value, and find that value: f(x) = 2x^2 - 16x - 42

Min = -74

500

Determine whether this function has a maximum or minimum value, and find that value: f(x) = 5 - 4x - 2x^2

Max = 7

Real Life Quadratics

100

A store rents 1400 videos per week at $2.25 per video. The owner estimates that they will rent 100 fewer videos for each $0.25 increase in price. What price will maximize the income of the store?

$2.88

200

A financial analyst determined that the cost, in thousands of dollars, of producing bicycle frames is C = 0.000025f^2 - 0.04f + 40, where f is the number of frames produced. Find the number of frames that minimizes the cost.

800

300

Omar owns a vending machine in a bowling alley. He currently sells 600 cans of soda per week at $0.65 per can. He estimates that he will lose 100 customers for every $0.05 increase in price and gain 100 customers for every $0.05 decrease in price. (The charge must be a multiple of 5) Write the quadratic equation for a price increase.

f(x) = -500x^2 - 3500x + 39,000

400

Omar owns a vending machine in a bowling alley. He currently sells 600 cans of soda per week at $0.65 per can. He estimates that he will lose 100 customers for every $0.05 increase in price and gain 100 customers for every $0.05 decrease in price. (The charge must be a multiple of 5) If Omar lowers the price, what should it be to maximize his income?

.40 or .50 cents

500

Omar owns a vending machine in a bowling alley. He currently sells 600 cans of soda per week at $0.65 per can. He estimates that he will lose 100 customers for every $0.05 increase in price and gain 100 customers for every $0.05 decrease in price. (The charge must be a multiple of 5) What will be his income per week if he maximizes his income?

$450/week

Potpourri

100

Find the vertex: f(x) = -4x^2 + 5x

5/8

200

What is Mr. Swayze's favorite food?

Sushi

300

Determine whether the function has a maximum or minimum value and find that value: f(x) = 8x - 3x^2 + 2

22/3

400

Spider-Man vs. Captain America

Stalemate

500

The 50th anniversary of the Star Trek franchise recently occurred. Which character in the series (not actor) attended Ole Miss?

Dr. Leonard McCoy