Quadratic Inequality Quiz

The video tutorial explains how to solve a quadratic inequality by first setting the inequality to zero, factoring the quadratic equation, and finding the solutions. It then demonstrates how to plot these solutions on a number line, test intervals, and express the solution using interval notation. Finally, the video verifies the solution graphically by highlighting the parts of the graph where the function is above or on the x-axis.

What is the first step in solving a quadratic inequality?

• Add a constant to both sides

• Multiply both sides by a constant

• Set the equation to zero

• Divide both sides by a variable

Which of the following is a factor of the quadratic equation x^2 - 4x - 60?

• x - 6

• x + 10

• x - 10

• x + 6

How are the roots of the quadratic equation represented on a number line when the inequality is 'greater than or equal to'?

• As closed points

• As arrows

• As open points

• As dashed lines

Which test value would you use to check the interval between the roots -6 and 10?

• x = -7

• x = 6

• x = 0

• x = 11

What is the result of substituting x = 11 into the inequality x^2 - 4x - 60 ≥ 0?

• Positive

• Undefined

• Zero

• Negative

What is the solution of the inequality x^2 - 4x - 60 ≥ 0 in interval notation?

• (-∞, -10] ∪ [6, ∞)

• (-∞, 6] ∪ [10, ∞)

• (-∞, -6) ∪ (10, ∞)

• (-∞, -6] ∪ [10, ∞)

How is the solution of the inequality expressed using inequalities?

• x > -6 and x < 10

• x ≤ -6 or x ≥ 10

• x < -6 or x > 10

• x ≥ -6 and x ≤ 10

What does it mean when a function is above the x-axis?

• The function is negative

• The function is zero

• The function is positive

• The function is undefined

What is the significance of the x-intercepts in the graph of the quadratic inequality?

• They are the minimum points

• They are the maximum points

• They are the points where the function is zero

• They are the points where the function is undefined

What is the purpose of graphically verifying the solution of a quadratic inequality?

• To determine the slope

• To identify the y-intercept

• To confirm the solution is correct

• To find the maximum value