Solving Quadratic Inequalities Graphically

The video tutorial explains how to solve the quadratic inequality 'x squared minus x minus twelve' less than or equal to zero. It covers solving the inequality by factoring the quadratic equation and testing intervals on a number line. The tutorial also demonstrates solving the inequality graphically by plotting the function and identifying when it is less than or equal to zero. The solution is found to be the closed interval from negative three to positive four.

What is the main goal when solving the quadratic inequality x^2 - x - 12 ≤ 0?

• To find the maximum value of x

• To calculate the derivative of the function

• To find all x values that satisfy the inequality

• To determine the vertex of the parabola

What are the roots of the equation x^2 - x - 12 = 0?

• x = 2 and x = -6

• x = 5 and x = -2

• x = 3 and x = -4

• x = 4 and x = -3

Why are the roots x = 4 and x = -3 important in solving the inequality?

• They are the points where the function is increasing

• They are the points where the inequality is undefined

• They are the maximum and minimum points of the function

• They are the points where the inequality changes sign

What is the purpose of forming intervals on the number line?

• To determine where the function is increasing

• To test which intervals satisfy the inequality

• To calculate the area under the curve

• To find the derivative of the function

Which test value is used for the interval to the left of x = -3?

• x = 5

• x = 0

• x = -4

• x = -2

What is the result of testing x = 0 in the inequality?

• The interval is partially true

• The interval is false

• The interval is undefined

• The interval is true

What is the solution interval for the inequality x^2 - x - 12 ≤ 0?

• [-3, 4]

• (-∞, -3)

• [4, ∞)

• (-3, 4)

How can the quadratic inequality be solved graphically?

• By calculating the area under the curve

• By plotting the function and identifying where it is above the x-axis

• By finding the derivative of the function

• By plotting the function and identifying where it is below or on the x-axis

What does it mean when the function is below or on the x-axis?

• The function values are less than or equal to zero

• The function is decreasing

• The function is increasing

• The function values are greater than zero

What is the advantage of solving the inequality graphically?

• It is more accurate

• It is faster and more straightforward

• It provides the exact roots

• It shows the maximum and minimum points