Understanding Domain and Range of Quadratic Functions

This video tutorial explains how to find the domain and range of quadratic functions. It covers the parent function y = x^2, transformations such as vertical and horizontal shifts, and how to handle quadratic functions in both vertex and standard forms. The video also discusses how to deal with non-factorable quadratics using the vertex formula. Key concepts include understanding the domain as all real numbers and determining the range based on the vertex and direction of the parabola.

What is the domain of the parent function y = x^2?

• 0 ≤ x ≤ 1

• x ≤ 0

• x ≥ 0

• All real numbers

For the function y = x^2, what is the range?

• y ≥ 0

• 0 ≤ y ≤ 1

• y ≤ 0

• All real numbers

How does the graph of y = -x^2 differ from y = x^2?

• It is reflected over the y-axis

• It is reflected over the x-axis

• It is shifted up

• It is shifted down

What is the range of the function y = -x^2?

• y ≥ 0

• y ≤ 0

• y ≤ 0 and includes 0

• y ≥ 0 and includes 0

If a quadratic function is shifted up by 4 units, how does the range change?

• The range remains the same

• The range starts at 0

• The range starts at 4

• The range starts at -4

What happens to the vertex of a quadratic function when it is shifted 3 units to the right?

• The x-coordinate of the vertex decreases by 3

• The y-coordinate of the vertex increases by 3

• The x-coordinate of the vertex increases by 3

• The y-coordinate of the vertex decreases by 3

For a quadratic function shifted 3 units left and 4 units down, what is the new vertex?

• (-3, -4)

• (3, -4)

• (3, 4)

• (-3, 4)

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

• Using the formula A/2B

• Using the formula -B/2A

• Using the formula B/2A

• Using the formula -A/2B

What is the range of a quadratic function with a vertex at (2, -3) that opens upwards?

• y ≥ -3

• y ≥ 3

• y ≤ 3

• y ≤ -3

If a quadratic function is not factorable, which method can be used to find the vertex?

• Using the formula -B/2A

• Graphing

• Using the quadratic formula

• Completing the square