Quadratic Inequalities and Graph Analysis

The video tutorial explains how to solve a quadratic inequality by converting it to standard form, finding critical points, and testing intervals. It demonstrates factoring the quadratic equation and analyzing the number line to determine the solution. The tutorial concludes with a graphical verification, showing that there are no solutions as the graph does not fall below the x-axis.

What is the first step in solving the quadratic inequality 3x^2 + 12x < -12?

• Subtract 12 from both sides

• Add 12 to both sides

• Multiply both sides by 3

• Divide both sides by 3

What is the greatest common factor that is factored out from 3x^2 + 12x + 12?

• 4

• 3

• 12

• 6

What is the critical point found when solving the equation 3(x + 2)^2 = 0?

• x = 2

• x = -2

• x = 0

• x = 3

Why is the critical point x = -2 plotted as an open point on the number line?

• Because the inequality is less than or equal to

• Because the inequality is less than

• Because x = -2 is part of the solution

• Because x = -2 is greater than 0

Which test value is used to the left of x = -2?

• x = 0

• x = 1

• x = -3

• x = -1

What is the result of testing x = -3 in the inequality 3(x + 2)^2 < 0?

• Undefined

• False

• True

• Cannot be determined

What is the result of testing x = 0 in the inequality 3(x + 2)^2 < 0?

• True

• False

• Cannot be determined

• Undefined

What conclusion is drawn from the number line analysis?

• The solution is x < -2

• The solution is x > -2

• There is no solution

• The solution is x = -2

What does the graph of y = 3x^2 + 12x + 12 indicate about the inequality?

• The graph is tangent to the x-axis

• The graph intersects the x-axis

• The graph is below the x-axis

• The graph is above the x-axis

What is the y-value at x = -2 on the graph of y = 3x^2 + 12x + 12?

• y = 12

• y = 2

• y = -2

• y = 0