Deck 10: Section 1: Quadratic Equations and Inequalities

Question 1

Find all real solutions of the given equation. (x² + 1)² - 18(x² + 1) = -17

A) {5, 3}
B) {0, 5, 3}
C) {0, ±4}
D) {±16}

Answer 1

{0, ±4}

Question 2

Find b² - 4ac and the number of real solutions for the given equation. x² + 3x + 4 = 0

A) -7, 2
B) 25, 0
C) -7, 0
D) 25, 2

Answer 2

-7, 0

Question 3

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 14 feet per second from a height of 7 feet. How long does it take to reach the earth?

A)
B)
C)
D)

Answer 3

Question 4

Solve:

A)
B) {4, 9}
C) {-4, -9}
D) {9}

Question 5

Solve by factoring: x² - x - 42 = 0

A) {-7, -6}
B) {-7, 6}
C) {-6, 7}
D) {6, 7}

Question 6

Complete the ordered pair so that it satisfies the given equation. y = x² - 10x - 5, (-10, )

A) (-10, 195)
B) (-10, 194)
C) (-10, 200)
D) (-10, 196)

Question 7

Terrence paddles his canoe upstream a distance of 4 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?

A) mph
B) mph
C) No real solution.
D) mph

Question 8

Solve:

A)
B)
C)
D)

Question 9

Write a quadratic equation that has the solutions -10 and 3.

A) x² + 7x - 30 = 0
B) x² + 30 = 0
C) x² - 60x - 30 = 0
D) x² + 60x - 30 = 0

Question 10

Find all real and imaginary solutions to the equation. x^-2 - 3x^-1 + 7 = 0

A)
B) {±3}
C) {3, ±3i}
D) {0, ±3}

Question 11

Find all real and imaginary solutions to the equation. b⁴ - 2401 = 0

A)
B) {0, ±7i}
C) {±7, ±7i}
D) {±7}

Question 12

Find the imaginary solutions: x² - 18x + 117 = 0

A) {9 + 6i, 9 - 6i}
B) {9 + 6i}
C) {-9 - 6i, 9 + 6i}
D) {9 + 6i, -9 + 6i}

Question 13

Solve by completing the square. 3x² - 8x + 2 = 0

A)

B)

C)

D)

Question 14

Find all real solutions of the given equation. x^2/3 - 2x^1/3 - 15 = 0

A) {±3, ±5}
B) {-27, 125}
C) {-3, 5}
D)

Question 15

Solve using the quadratic formula: 3x² + 5x - 7 = 0

A)

B)

C)

D)

Question 16

Which of the following is the correct graph of ?

A)

B)

C)

D)

Question 17

Use the discriminant to determine whether the given quadratic polynomial can be factored, then factor it if it is not prime. 10x² + 10x + 6

A) The expression is prime.
B) (x + 10)(x + 6)
C) (10x + 6)(x + 10)
D) (10x + 10)(x + 6)

Question 18

Find the vertex for the graph of the parabola. f(x) = x² - 15

A) (-15, 0)
B) (0, -15)
C)
D) (0, 0)

Question 19

Solve: (x - 7)² = 100

A) {-3, 17}
B) {3, 17}
C) {-3, 3}
D) {17, 17}

Question 20

Find all intercepts for the graph of the parabola. f(x) = 25 - x²

A) (0, 0), (5, 25)
B) (0, 25), (-5, 0), (5, 0)
C) (25, 0), (0, -5), (0, 5)
D) (0, 25), (5, 0)

Question 21

The monthly profit P in dollars that Carla makes on the sale of x automobiles is determined by the formula P = x² + 3x - 54. For what values of x is her profit positive?

A) 6, 7, ...
B) 1, 2, ..., 7
C) 7, 8, ...
D) 1, 2, ..., 6

Question 22

Solve the inequality. Graph the solution set. x² - 12x + 32 < 0

A)
B)
C)
D)

Question 23

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) = 0.01x² - 2.4x + 224. What number of batteries per hour minimizes the cost?

A) 224 batteries
B) 130 batteries
C) 80 batteries
D) 120 batteries

Question 24

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

A)
B) (-10, 0] $\cup$ [0, 1)
C) [-10, 1)
D) (-10, 1]

Question 25

Solve the given inequality and express the solution in interval notation. x² + 9x $\ge$ 0

A) (- $\infty$ , 0] $\cup$ [9, $\infty$ )
B) [0, $\infty$ )
C) [-9, 0]
D) (- $\infty$ , -9] $\cup$ [0, $\infty$ )