Understanding the Range of a Quadratic Function

Mr. B explains how to find the range of a quadratic function by determining if the graph opens up or down, using the leading coefficient. He describes the vertex as a key point, with its y-coordinate determining the range. The video includes a step-by-step example of finding the range for a specific quadratic equation, emphasizing the importance of the vertex's y-coordinate in defining the range.

What is the range of a quadratic function?

• The set of all possible a-values

• The set of all possible x-values

• The set of all possible y-values

• The set of all possible z-values

What determines if a quadratic graph opens upwards?

• The leading coefficient is one

• The leading coefficient is positive

• The leading coefficient is negative

• The leading coefficient is zero

In a quadratic function, what is the vertex?

• The midpoint of the graph

• The highest or lowest point on the graph

• The point where the graph intersects the y-axis

• The point where the graph intersects the x-axis

How do you find the x-coordinate of the vertex in a quadratic function?

• Using the formula -b/a

• Using the formula -b/2a

• Using the formula b/2a

• Using the formula a/b

What is the range of the quadratic function y = -2x^2 + 4x + 1?

• y ≤ 1

• y ≥ 1

• y ≤ 3

• y ≥ 3

If a quadratic graph opens downwards, what can be said about its range?

• y is not related to the y-coordinate of the vertex

• y is less than or equal to the y-coordinate of the vertex

• y is greater than or equal to the y-coordinate of the vertex

• y is equal to the y-coordinate of the vertex

What is the significance of the y-coordinate of the vertex in determining the range?

• It is the midpoint of the y-values

• It is the average y-value of the graph

• It is the maximum or minimum y-value of the graph

• It is irrelevant to the range

What is the first step in finding the range of a quadratic function?

• Determine the x-intercepts

• Calculate the slope

• Identify if the graph opens up or down

• Find the y-intercepts

What happens to the range if the quadratic graph opens upwards?

• y is not affected by the vertex

• y is less than or equal to the y-coordinate of the vertex

• y is greater than or equal to the y-coordinate of the vertex

• y is equal to the y-coordinate of the vertex

What is the final step in determining the range of a quadratic function?

• Determine the direction of the graph

• Calculate the slope

• Find the x-coordinate of the vertex

• Find the y-coordinate of the vertex