Understanding Quadratic Functions and Inequalities

The video tutorial explains how to graph a quadratic inequality, focusing on the inequality y ≥ -x² + 2x + 3. It covers the steps to graph the corresponding quadratic function, identify the axis of symmetry and vertex, and find the y-intercept and x-intercepts. The tutorial also demonstrates how to graph the parabola, determine the shaded region based on the inequality, and verify the solution using a test point.

What does the inequality symbol 'greater than or equal to' indicate about the graph of the parabola?

• The graph will be dotted.

• The graph will be invisible.

• The graph will be dashed.

• The graph will be solid.

In the quadratic function y = ax^2 + bx + c, what is the role of 'a'?

• It determines the y-intercept.

• It affects the direction of the parabola.

• It has no effect on the graph.

• It is the constant term.

How do you find the x-coordinate of the vertex in a quadratic function?

• By using the formula x = -b/2a.

• By setting y to zero.

• By solving the equation for x.

• By finding the y-intercept.

What is the y-coordinate of the vertex for the function y = -x^2 + 2x + 3?

• 0

• 3

• 4

• 1

How do you determine the y-intercept of a quadratic function?

• By setting x to zero.

• By setting y to zero.

• By finding the vertex.

• By solving for x.

What are the x-intercepts of the function y = -x^2 + 2x + 3?

• (0, 3) and (2, 3)

• (3, 0) and (-1, 0)

• (1, 4) and (0, 3)

• (2, 0) and (3, 0)

Why is the graph of the parabola solid in this inequality?

• Because the parabola is downward.

• Because the parabola is upward.

• Because the inequality includes 'equal to'.

• Because the inequality is strict.

Where should the shading be applied for the inequality y ≥ -x^2 + 2x + 3?

• Inside the parabola.

• Below the parabola.

• On the parabola.

• Above the parabola.

What is the purpose of selecting a test point when graphing inequalities?

• To find the vertex.

• To calculate the axis of symmetry.

• To verify the shaded region is correct.

• To determine the y-intercept.

Which point is used as a test point in the video to verify the shaded region?

• (3, 0)

• (4, 0)

• (0, 3)

• (1, 4)