To graph $y > x^2 + 1$, you test the point $(0,0)$. What is the result of this test and which region should be shaded?

True; shade the region containing (0,0)

False; shade the region containing (0,0)

True; shade the region not containing (0,0)

False; shade the region not containing (0,0)

Which statement correctly describes the graph of the inequality $y < -x^2 + 4$?

A dashed parabola shaded below.

A dashed parabola shaded above.

Quadratic Inequalities Practice — Grade 8 math

Lesson 6: Quadratic Inequalities — Practice Questions

1. Which of the following inequalities would be graphed with a solid boundary curve?
- A. $y > x^2 - 5$
- B. $y < -x^2 + 3$
- C. $y \geq x^2 + 1$
- D. $x^2 + y^2 > 25$
2. To graph $y > x^2 + 1$, you test the point $(0,0)$. What is the result of this test and which region should be shaded?
- A. True; shade the region containing (0,0)
- B. False; shade the region containing (0,0)
- C. True; shade the region not containing (0,0)
- D. False; shade the region not containing (0,0)
3. The graph of the inequality $x^2 + y^2 < 16$ has a dashed boundary. To determine the shaded region, the point $(0,0)$ is tested and found to be a solution. Therefore, the region ___ the circle is shaded.
4. The point $(3, k)$ is a solution to the inequality $y \leq x^2 - 6$. The greatest possible integer value for $k$ is ___.
5. Which statement correctly describes the graph of the inequality $y < -x^2 + 4$?
- A. A solid parabola shaded above.
- B. A dashed parabola shaded below.
- C. A solid parabola shaded below.
- D. A dashed parabola shaded above.
6. Which statement best describes the solution set of the inequality $y > x^2 + 2x - 8$?
- A. All points on the parabola $y = x^2 + 2x - 8$.
- B. All points below the parabola $y = x^2 + 2x - 8$.
- C. All points above the parabola $y = x^2 + 2x - 8$.
- D. All points on or below the parabola $y = x^2 + 2x - 8$.
7. When graphing the inequality $y \leq -x^2 + 6x$, what type of line should be used for the boundary parabola?
- A. A solid line
- B. A dashed line
- C. A vertical line
- D. A horizontal line
8. For the point $(2, y)$ to be a solution to the inequality $y < x^2 - 3x + 5$, the value of $y$ must be less than ___.
9. Which inequality represents the region of all points on or below the parabola defined by $y = 3x^2 - 12x + 7$?
- A. $y < 3x^2 - 12x + 7$
- B. $y > 3x^2 - 12x + 7$
- C. $y \geq 3x^2 - 12x + 7$
- D. $y \leq 3x^2 - 12x + 7$
10. The point $(4, k)$ is on the boundary parabola of the inequality $y \geq -x^2 + 5x - 2$. What is the value of $k$? ___