Deck 10: Section 2: Quadratic Equations and Inequalities

Question 1

Find all real and imaginary solutions to the equation.
x^-2 - 3x^-1 + 5 = 0

Answer 1

Question 2

Solve:

Answer 2

Question 3

Find all intercepts for the graph of the parabola.
f(x) = 49 - x²

Answer 3

(0, 49), (-7, 0), (7, 0)

Question 4

Solve:

Question 5

Graph the parabola.
y = -x² + 4

Question 6

Use the discriminant to determine whether the given quadratic polynomial can be factored, then factor it if it is not prime.
7x² + 7x + 9

Question 7

Find all real solutions of the given equation.
x^2/3 - 3x^1/3 - 10 = 0

Question 8

Find all real solutions of the given equation.
(x² + 1)² - 11(x² + 1) = -10

Question 9

Solve: (q - 6)² = 36

Question 10

Terrence paddles his canoe upstream a distance of 6 miles. He completes the return trip in 30 minutes less that the upstream journey. If the current flows at 4 miles per hour, what is Terrence's speed in still water?

Question 11

Complete the ordered pair so that it satisfies the given equation.
y = x² + 4x + 2, (4, )

Question 12

Find b² - 4ac and the number of real solutions for the given equation.
x² - 2x + 1 = 0

Question 13

If an object is given an initial velocity of v₀ feet per second from a height of s₀ feet, then its height S after t seconds is given by the formula . A rock is thrown into the air at 42 feet per second from a height of 21 feet. How long does it take to reach the earth?

Question 14

Solve by factoring: x² - 5x - 50 = 0

Question 15

Solve by completing the square.
2x² - 5x + 1 = 0

Question 16

Write a quadratic equation that has the solutions 8 and 1.

Question 17

Find the vertex for the graph of the parabola.
f(x) = x² - 5

Question 18

Find the imaginary solutions: x² - 6x + 90 = 0

Question 19

Find all real and imaginary solutions to the equation.
t⁴ - 6561 = 0

Question 20

Solve using the quadratic formula: 3x² + 5x - 1 = 0

Question 21

Solve the given inequality and express the solution in interval notation.
x² - 4x $\ge$ 0

Question 22

A battery manufacturing plant spends C dollars per hour to produce "D"-size batteries. An efficiency consultant has determined that C is related to the number of batteries produced per hour, x, according to the equation C(x) = 0.02x² - 3x + 217.5. What number of batteries per hour minimizes the cost?

Question 23

Solve the given inequality and express the solution in interval notation.

Question 24

The monthly profit P in dollars that Carla makes on the sale of x automobiles is determined by the formula P = x² - 6x - 7. For what values of x is her profit positive?

Question 25

Solve the inequality. Graph the solution set.
x² - 8x + 12 < 0