Illustrating Quadratic Inequality

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

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