Understanding Quadratic Functions and Graphing

This lesson demonstrates how to create artwork by graphing quadratic equations with domain restrictions. The video explains the role of parameters 'a' and 'd' in shaping the parabola and shows how to use Desmos to animate and customize graphs. It covers setting domain restrictions and using sliders to adjust graph parameters, ultimately creating a simple yet symmetrical piece of art. The tutorial encourages exploring more equations and restrictions for intricate designs.

What does the parameter 'a' in the equation y = ax^2 + d determine?

• The horizontal shift

• The vertical stretch or compression

• The color of the graph

• The domain restriction

If 'a' is negative in the equation y = ax^2 + d, how does the parabola open?

• To the right

• Upwards

• To the left

• Downwards

What is the purpose of using domain restrictions in graphing quadratic equations?

• To determine the graph's thickness

• To adjust the vertical shift

• To limit the range of x-values

• To change the color of the graph

How many quadratic equations were used to create the artwork in the demonstration?

• 8

• 10

• 5

• 12

What happens when you click the wrench icon and select reverse contrast in Desmos?

• The graph becomes invisible

• The coordinate plane turns black and the graph turns white

• The graph's color changes to red

• The graph rotates 90 degrees

How many color options are available for changing the graph's appearance in Desmos?

• Four

• Seven

• Five

• Six

What is the range of values for 'b' in the domain restrictions used in the artwork?

• From -1 to 1

• From -3 to 3

• From -2 to 2

• From 0 to 4

What feature allows you to adjust the upper bound of the domain restriction in Desmos?

• A zoom tool

• A slider

• A color picker

• A rotation tool

What pattern can be observed in the equations used to create the artwork?

• They all have the same 'a' value

• They all have the same domain restrictions

• They all have different colors

• They all have the same 'd' value

What can be done to create a more intricate piece of artwork using quadratic equations?

• Use fewer equations

• Add more equations and domain restrictions

• Limit the domain to a single value

• Use only positive 'a' values