Key Features of Quadratic Functions Explained

This lesson covers the key features of quadratic functions, including y-intercepts, x-intercepts, and vertices. It provides examples of parabolas with different characteristics, such as those with no x-intercepts and those tangent to the x-axis. The lesson also explains the concept of end behavior, describing how the function values behave as x approaches positive or negative infinity. Practice problems are included to reinforce the concepts, and the lesson concludes with a discussion on counterexamples to common assumptions about quadratic functions.

What is the y-intercept of a parabola that does not intersect the x-axis?

• (0, -2)

• (0, 2)

• (0, 0)

• (1, -1)

If a parabola has a vertex at (1, -1) and opens downwards, what is the nature of the vertex?

• Minimum

• Maximum

• Undefined

• Neither

What is the x-intercept of a parabola that just touches the x-axis and turns around?

• (0, 0)

• (-3, 0)

• (3, 0)

• (0, -3)

Where does a parabola intersect the y-axis if the y-intercept is (0, 9)?

• At (0, -9)

• At (9, 0)

• At the origin

• Between 5 and 10 on the y-axis

If a parabola's vertex is also its x-intercept, what can be inferred about the vertex?

• It is a maximum

• It is undefined

• It is a minimum

• It is neither maximum nor minimum

What is the x-intercept of a parabola whose vertex is at the top of the curve?

• It has multiple x-intercepts

• It has two x-intercepts

• It has one x-intercept

• It does not have an x-intercept

In a parabola opening downwards, what is the end behavior as x approaches positive infinity?

• Y remains constant

• Y goes to positive infinity

• Y goes to negative infinity

• Y oscillates

What does the end behavior of a function describe?

• The vertex of the function

• The direction of the function values as x increases or decreases

• The intercepts of the function

• The maximum and minimum points

Which of the following is true for the end behavior of a parabola opening upwards?

• Y values go to negative infinity as x goes to positive infinity

• Y values remain constant

• Y values go to positive infinity as x goes to positive infinity

• Y values go to positive infinity as x goes to negative infinity

What is the y-coordinate of the vertex for a parabola with vertex at (2, 1)?

• 1

• 0

• -1

• 2