Question 1

Which of the following is the correct first step to solve the inequality $$x^2 - 4x$$ \u003e 0$$?

Accepted Answer

Move all terms to the left side so the right side is 0.

Question 2

Given the quadratic inequality $$x^2 - 4x$$ \u003e 0$$, which intervals represent the solution set?

Accepted Answer

$$(-\infty, 0) \cup (4, \infty)$$

Question 3

For the inequality $$x^2 + 4x + 3$$ \geq 0$$, which of the following describes the correct solution set?

Accepted Answer

$$(-\infty, -3] \cup [-1, \infty)$$

Question 4

If a quadratic function $$f(x) = ax^2$ + bx + c$$ opens upwards and has two real x-intercepts, for which values of $$x is$$ $$f(x) \u003c 0$$?

Accepted Answer

For $$x$$ between the two x-intercepts.

Question 5

Solve the inequality $$x^2 - x - 2$$ \leq 0$$.

Accepted Answer

$$[-2, 1]$$

Question 6

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 1. $$For which values of $$t is $$the ball at least 16 meters above the ground?

Accepted Answer

$$1 \leq t \leq 3$$

Question 7

Which of the following best describes the solution to $$x^2 + 1$$ \u003c 0$$?

Accepted Answer

No real solution.

Question 8

Given the inequality $$x^2 - 6x + 9$$ \geq 0$$, what is the solution set?

Accepted Answer

$$(-\infty, 3] \cup [3, \infty)$$

Question 9

If $$f(x) = x^2$ - 4x + 3$$, for which $$x is$$ $$f(x) \u003c 0$$?

Accepted Answer

$$(1, 3)$$

Question 10

A company’s profit $$P(x) in $$thousands of dollars is modeled by $$P(x) = -2x^2$ + 8x - 6$$, where $$x is $$the number of units sold in hundreds. For which values of $$x is $$the company making a profit (i.e., $$P(x) \u003e 0$$)?

Accepted Answer

$$(1, 3)$$

Question 11

Which of the following is true about the solution to $$x^2 - 2x + 1$$ \leq 0$$?

Accepted Answer

$$x = 1$$

Question 12

If a quadratic function $$f(x) = ax^2$ + bx + c$$ has no real x-intercepts, what can you conclude about the solution to $$f(x) \u003e 0$$?

Accepted Answer

The solution is all real numbers if $$a \u003e 0.$$

Question 13

Solve the inequality $$-x^2 + 2x + 3$$ \u003e 0$$.

Accepted Answer

$$(-1, 3)$$

Question 14

Which of the following best describes the solution to $$x^2 - 5x + 6$$ \u003c 0$$?

Accepted Answer

$$(2, 3)$$

Question 15

A medical researcher models the concentration of a drug in the bloodstream by $$C(t) = -t^2$ + 6t + 5$$, where $$t is $$hours after administration. For which $$t is $$the concentration at least 14 mg/L?

Accepted Answer

$$1 \leq t \leq 5$$

Question 16

Which of the following is the correct interpretation of the solution to $$x^2 - 9$$ \leq 0$$?

Accepted Answer

$$[-3, 3]$$

Solving Inequalities Involving Quadratic Functions

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