Graphing Quadratic Inequalities

This video tutorial explains how to graph the solution to a quadratic inequality. It begins by introducing the inequality y ≤ -x² - 1 and describes how to graph the corresponding parabola. The tutorial covers the difference between solid and dashed graphs based on the inequality symbol. It then demonstrates how to determine the solution region by selecting a test point and shading the appropriate area. The video concludes with a summary of the solution process.

What is the first step in graphing the solution to the inequality y ≤ -x² - 1?

• Shade the region above the parabola

• Graph y = -x² - 1

• Find the x-intercepts

• Determine the vertex of the parabola

Why is the graph of y = -x² - 1 solid?

• Because it is a linear equation

• Because y is greater than -x² - 1

• Because y is less than or equal to -x² - 1

• Because it is a dashed line

How is the graph of y = -x² - 1 related to y = x²?

• It is stretched vertically

• It is shifted up one unit

• It is reflected over the y-axis

• It is reflected over the x-axis and shifted down one unit

What is the y-coordinate when x = 0 for the equation y = -x² - 1?

• -2

• 1

• 0

• -1

Which points are used to graph the parabola y = -x² - 1?

• (0,-1), (2,-5), (-2,-5)

• (0,0), (1,-1), (-1,-1)

• (0,-1), (1,-2), (-1,-2)

• (0,1), (2,3), (-2,3)

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

• To find the vertex of the parabola

• To calculate the x-intercepts

• To determine the slope of the line

• To check which region satisfies the inequality

Which test point is commonly used to determine the shading region?

• (1,1)

• (0,0)

• (-1,-1)

• (2,2)

What does it mean if the test point does not satisfy the inequality?

• Shade the region opposite to the test point

• Shade the region containing the test point

• Do not shade any region

• The graph is incorrect

What conclusion can be drawn if a point lies in the shaded region?

• The point is on the x-axis

• The point is on the y-axis

• The point satisfies the inequality

• The point does not satisfy the inequality

What does the shaded region represent in the context of the inequality y ≤ -x² - 1?

• The solution set of the inequality

• The area where y is positive

• The area where x is positive

• The area where y is greater than -x² - 1