Understanding Parabolas and Their Properties

This video tutorial explains the key features of quadratic graphs, focusing on parabolas. It covers the concepts of x-intercepts, roots, zeros, and solutions, and demonstrates how to identify these features on a graph. The tutorial also explains how to find the vertex, axis of symmetry, and determine if a parabola has a maximum or minimum point. Two examples are provided to illustrate these concepts, helping students understand how to analyze and label quadratic graphs effectively.

What is the graph of a quadratic function called?

• Ellipse

• Hyperbola

• Circle

• Parabola

Which of the following terms is NOT synonymous with x-intercepts?

• Roots

• Zeros

• Solutions

• Vertices

How many x-intercepts can a parabola have?

• One

• Two

• None

• All of the above

Where is the vertex of a parabola located?

• At the top of the U-shape

• At the intersection of the y-axis

• At the midpoint of the x-axis

• At the bottom of the U-shape

How do you write the axis of symmetry for a parabola?

• x = a number

• y = mx + b

• y = a number

• x = my + b

What does it mean if a parabola has a minimum?

• It has no x-intercepts

• It opens downwards

• It has two x-intercepts

• It opens upwards

In the first example, what are the coordinates of the vertex?

• (-2, 3)

• (-2, -3)

• (-4, 0)

• (0, 0)

In the second example, what are the coordinates of the vertex?

• (-1, 0)

• (-3, -4)

• (-5, 0)

• (-3, 4)

What is the axis of symmetry in the second example?

• x = 4

• x = -3

• x = -1

• x = -5

Does the parabola in the second example have a maximum or a minimum?

• Maximum

• Minimum

• Both

• Neither