Graphing Parabolas and Inequalities

This video tutorial explains how to graph the solution to a quadratic inequality on a coordinate plane. It covers the steps to graph the parabola, determine whether to use a dashed or solid line, and find the vertex and intercepts. The tutorial also demonstrates how to use test points to identify the solution region and verify the inequality. The example uses the inequality y > x^2 - 4, and the process involves graphing y = x^2 - 4, using a dashed line, and testing points to determine the shaded region inside the parabola.

What is the first step in graphing the solution to the inequality y > x^2 - 4?

• Find the vertex of y = x^2 - 4

• Shade the region above y = x^2 - 4

• Graph the curve y = x^2 - 4

• Graph the line y = x^2 - 4

Why is the graph of the parabola y = x^2 - 4 dashed?

• Because y is equal to x^2 - 4

• Because y is less than x^2 - 4

• Because y is greater than x^2 - 4

• Because y is greater than or equal to x^2 - 4

How is the graph of y = x^2 - 4 related to y = x^2?

• Shifted left 4 units

• Shifted down 4 units

• Shifted up 4 units

• Shifted right 4 units

What is the vertex of the parabola y = x^2 - 4?

• (0, -4)

• (-2, 0)

• (0, 0)

• (2, 0)

Which point is used as a test point to determine the shading region?

• (0, 0)

• (1, 1)

• (-1, -1)

• (2, 2)

What do you do if the test point satisfies the inequality?

• Do not shade any region

• Shade both regions

• Shade the opposite region

• Shade the same region as the test point

What is the inequality used to test the point (0,0)?

• 0 < 0^2 - 4

• 0 ≤ 0^2 - 4

• 0 > 0^2 - 4

• 0 = 0^2 - 4

What conclusion is drawn if the test point (0,0) satisfies the inequality?

• The solution is on the parabola

• The solution is inside the parabola

• The solution is outside the parabola

• The solution is not determined

What happens if a test point does not satisfy the inequality?

• Shade the region containing the test point

• Do not shade any region

• Shade the region not containing the test point

• Shade both regions

What is the final solution region for the inequality y > x^2 - 4?

• On the parabola

• No solution

• Outside the parabola

• Inside the parabola