Quadratic Inequalities and Functions

The video tutorial explains how to solve a quadratic inequality, specifically 2x^2 - 7x > 0, using interval notation. It begins by setting the inequality in standard form and finding critical points by factoring. The number line is divided into intervals, and test points are used to determine which intervals satisfy the inequality. The solution is expressed in interval notation and verified graphically by analyzing the quadratic function's graph.

What is the first step in solving a quadratic inequality?

• Graphing the inequality

• Setting the inequality in standard form

• Finding the vertex of the parabola

• Calculating the discriminant

How do you find the critical points of the quadratic equation 2x^2 - 7x = 0?

• By completing the square

• By graphing the equation

• By using the quadratic formula

• By factoring the equation

What type of points are used on the number line for inequalities with 'greater than' symbols?

• Dashed points

• Solid points

• Open points

• Closed points

Which test point would you use for the interval to the left of x = 0?

• x = 1

• x = 0

• x = 4

• x = -1

What is the result of testing x = 1 in the inequality 2x^2 - 7x > 0?

• True, the interval is part of the solution

• False, the interval is not part of the solution

• False, but the interval is part of the solution

• True, but the interval is not part of the solution

What is the interval notation for the solution of the inequality 2x^2 - 7x > 0?

• (-∞, 0) ∪ (7/2, ∞)

• [0, ∞)

• [0, 7/2]

• (-∞, 7/2]

Why are parentheses used in the interval notation for the solution?

• Because the endpoints are included

• Because the solution is a closed interval

• Because the solution is a single point

• Because the endpoints are not included

What does the graph of the quadratic function indicate about the solution?

• The solution is where the graph is above the x-axis

• The solution is where the graph is below the x-axis

• The solution is at the x-intercepts

• The solution is at the vertex of the parabola

What are the x-intercepts of the quadratic function y = 2x^2 - 7x?

• x = 0 and x = 3.5

• x = 0 and x = 7

• x = 3.5 and x = 7

• x = 1 and x = 4

What does the graphical verification confirm about the solution?

• The solution needs adjustment

• The solution is incorrect

• The solution is partially correct

• The solution is correct