WorksheetsIllustrating Quadratic Inequality
Total questions: 10
Worksheet time: 8mins
It is an inequality that can be written in any of the following forms:
𝑎𝑥2 + 𝑏𝑥 + 𝑐 > 0, 𝑎𝑥2 + 𝑏𝑥 + 𝑐 < 0, 𝑎𝑥2 + 𝑏𝑥 + 𝑐 ≥ 0 or 𝑎𝑥2 + 𝑏𝑥 + 𝑐 ≤ 0.
Quadratic Equation
Quadratic Inequality
Linear Inequality
Linear Equation
Which of the following mathematical statements is a quadratic inequality?
2𝑟2 − 3𝑟 − 5 = 0
7ℎ + 12 < 0
3𝑡2 + 7𝑡 + 2 ≥ 0
𝑠2 + 8𝑠 + 15 = 0
Which of the following is NOT true about quadratic inequality?
It always contains a linear expression.
It contains a 2nd degree polynomial.
Two sides of the inequality separated by <, >, ≥ or ≤.
None of the above
Which of the following shows a relation of “greater than or equal to”?
(𝑥 + 4)2 < 2𝑥
(𝑥 + 4)2 > 2𝑥
𝑥2 + 4 ≥ 2𝑥
𝑥2 + 4 ≤ 2𝑥
Which of the following is a quadratic inequality?
𝑏 > 9
𝑐2 − 4𝑥 ≥ 𝑐2 + 8
𝑣(𝑣 + 7) < 𝑣2 + 8
𝑥2 + 8 < −4𝑥
The monthly profit 𝑃 of Karen’s business is represented by the equation 𝑃(𝒙) = 𝑥2 + 100. Which of the following quadratic inequalities is a representation of positive profit for Karen’s business?
𝑥2 + 100 ≥ 0
𝑥2 + 100 ≤ 0
−𝑥2 + 100 > 0
−𝑥2 + 100 < 0
The monthly profit 𝑃 of Karen’s business is represented by the equation 𝑃(𝒙) = 𝑥2 + 100. Which of the following is a representation of negative or normal profit for Karen’s business?
𝑥2 + 100 ≥ 0
𝑥2 + 100 ≤ 0
𝑥2 + 100 > 0
𝑥2 + 100 < 0
The floor of a conference hall can be covered completely with tiles. Its length is 36 ft longer than its width. The area of the floor is less than 2,040 square feet. What mathematical sentence would represent the given situation?
𝑥2 − 36 < 2040
𝑥2 + 36 < 2040
𝑥2 − 36𝑥 > 2040
𝑥2 + 36𝑥 < 2040
Which of the following is NOT a quadratic inequality?
3(2𝑤2 − 5) < 𝑤
6(𝑣2 − 2) − 4𝑣 < 0
4𝑥2 − 9 ≥ 0
x+22x−5≤0
An open box is to be formed out a rectangular piece of cardboard whose length is 12 cm longer than its width. To form the box, a square of side 5 cm will be removed from each corner of the cardboard. Then the edges of the remaining cardboard will be turned up. If the box is to hold at most 1900𝑐𝑚3 , what mathematical statement would represent the given situation?
𝑥2 − 12𝑥 ≤ 360
𝑥2 − 12𝑥 ≤ 380
𝑥2 − 8𝑥 ≤ 400
𝑥2 − 17𝑥 ≤ 310
