Question 1

Which of the following is the correct first step when solving a quadratic inequality such as $$x^2 - 4$$ \u003c 0$$?

Accepted Answer

Set the inequality equal to zero: $$x^2 - 4 = 0$

Question 2

Given the quadratic inequality $$1 - x^2$ \u003c 0$$, what is the solution in interval notation?

Accepted Answer

$$(-\infty, -1) \cup (1, \infty)$$

Question 3

After factoring $$x^2 - 4 = 0$, what are the critical points used to test intervals for the inequality x^2$ - 4 \u003c 0$$?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 4

Which test value would you use to check the interval $$(-\infty, -2)$$ for the inequality $$x^2 - 4$$ \u003c 0$$?

Accepted Answer

$$x = -3$$

Question 5

If you solve $$\frac{1}{8}x^2$ + x + 2 \geq 0$$ and find that all test values are true, what is the solution set?

Accepted Answer

All real numbers

Question 6

Which of the following best describes the graphical approach to solving quadratic inequalities?

Accepted Answer

Finding where the graph of the quadratic is above or below the x-axis.

Question 7

For the inequality $$x^2 - 4$$ \u003e 0$$, which intervals should be tested?

Accepted Answer

$$(-\infty, -2)$$ and $$(2, \infty)$$

Question 8

A chemical reaction is modeled by $$T^2 - 16T + 63$$ \u003c 0$$, where T$ is temperature in degrees Celsius. For which temperature range is the reaction rate negative?

Accepted Answer

$$(7, 9)$$

Question 9

Which of the following is NOT a correct step in solving quadratic inequalities?

Accepted Answer

Multiply both sides by a negative number without reversing the inequality.

Question 10

If the quadratic $$ax^2 + bx + c$ opens upwards and the inequality is ax^2$ + bx + c \u003c 0$$, where will the solution set be located?

Accepted Answer

Between the two real roots

Question 11

Given $$x^2 + 4x + 3$$ \leq 0$$, what is the solution in interval notation?

Accepted Answer

$$[-3, -1]$$

Question 12

A projectile's height is modeled by $$h(t) = -16t^2$ + 32t + 48. $$For which values of $$t is $$the height above 64 feet?

Accepted Answer

$$(1, 3)$$

Question 13

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

Accepted Answer

$$x \leq -3 or$$ $$x \geq 3$$

Question 14

If a quadratic inequality has no real solutions, what does this mean graphically?

Accepted Answer

The parabola does not cross the x-axis in the region of interest.

Quadratic Inequalities: Algebraic and Graphical Approaches

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