Understanding Quadratic Functions

This video tutorial covers graphing quadratic functions by plotting points. It begins with an introduction to the function f(x) = x² - 3, explaining how to set up a table of values by selecting inputs and calculating corresponding outputs. The tutorial demonstrates plotting these points on a Cartesian plane and discusses the properties of the resulting quadratic graph, including its symmetry and intercepts. Finally, the video shows how to verify the graph using a graphing calculator.

What is the function rule for f(x) = x² - 3?

• Subtract 3 from the input

• Add 3 to the square of the input

• Subtract 3 from the square of the input

• Multiply the input by 3

Which of the following is a correct input value for graphing f(x) = x² - 3?

• 4

• -3

• 5

• 0

What is the output when the input is -2 for the function f(x) = x² - 3?

• 4

• 1

• -1

• 3

Which ordered pair is correct for the input 1 in the function f(x) = x² - 3?

• (1, -2)

• (1, -3)

• (1, 2)

• (1, 0)

What is the output for the input 3 in the function f(x) = x² - 3?

• 3

• 6

• 9

• 0

What shape does the graph of f(x) = x² - 3 form?

• Parabola

• Ellipse

• Line

• Circle

Where does the graph of f(x) = x² - 3 intersect the vertical axis?

• (0, 3)

• (0, 0)

• (0, 1)

• (0, -3)

What is a characteristic of the graph of f(x) = x² - 3?

• It is asymmetrical

• It has no intercepts

• It is a straight line

• It is symmetrical across the vertical axis

What should you do to verify the graph on a graphing calculator?

• Press Zoom 3

• Press Zoom 6

• Press Zoom 1

• Press Zoom 9

What is the purpose of verifying the graph with a graphing calculator?

• To change the function

• To find new inputs

• To adjust the scale

• To ensure the graph is correct