Understanding Quadratic Functions and Inequalities

The video tutorial explains how to graph the solution to a quadratic inequality. It begins by introducing the inequality and its implications for graphing, such as using a dashed line for the parabola. The tutorial then covers graphing the corresponding quadratic function in vertex form, identifying the vertex, and finding the vertical and horizontal intercepts. The process of plotting points and graphing the parabola is demonstrated, emphasizing the axis of symmetry. Finally, the tutorial explains how to determine and shade the solution region, verifying it with a test point.

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

• The graph is solid.

• The graph is dashed.

• The graph is a straight line.

• The graph is shaded below.

In the vertex form of a quadratic function, what does the 'h' in (x - h) represent?

• The slope of the parabola

• The x-coordinate of the vertex

• The y-intercept of the parabola

• The y-coordinate of the vertex

What does the vertex of the parabola represent in the graph?

• The point where the graph intersects the x-axis

• The point where the graph intersects the y-axis

• The lowest point of the graph

• The highest point of the graph

Tags

CCSS.HSF-IF.C.7A

What is the y-intercept of the quadratic function y = (x + 3)^2 - 4?

• (0, -4)

• (0, 5)

• (0, 9)

• (0, 3)

Tags

CCSS.HSF-IF.C.7A

How does the axis of symmetry help in plotting additional points on the graph?

• It allows plotting points only on one side.

• It helps in finding the vertex.

• It allows plotting symmetric points on both sides.

• It divides the graph into two unequal parts.

Tags

CCSS.HSF-IF.C.7A

What are the x-intercepts of the quadratic function y = (x + 3)^2 - 4?

• (-1, 0) and (-5, 0)

• (0, -1) and (0, -5)

• (1, 0) and (5, 0)

• (-3, 0) and (3, 0)

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CCSS.HSA.REI.D.12

Why is the graph of the parabola dashed?

• Because the inequality is 'equal to'.

• Because the inequality is 'greater than'.

• Because the inequality is 'less than'.

• Because the inequality is 'greater than or equal to'.

Tags

CCSS.HSF-IF.C.7A

Where should the shading be applied for the inequality y > (x + 3)^2 - 4?

• Below the parabola

• Above the parabola

• Outside the parabola

• On the parabola

Tags

CCSS.HSA.REI.D.12

What is the purpose of selecting a test point in the region of the graph?

• To find the x-intercepts

• To check the axis of symmetry

• To verify the vertex

• To confirm the shading region

Tags

CCSS.HSA.REI.D.12

Which point was used to verify the shading region in the graph?

• (-1, 0)

• (0, 5)

• (-3, 0)

• (-5, 0)

Tags

CCSS.HSA.REI.D.12