Graphing Quadratics in Vertex Form: Rate of Change Insights

What is the rate of change in a linear function as x increases by 1?

• It increases by odd numbers

• It decreases over time

• It remains constant

• It varies depending on the function

How does the rate of change behave in a parent quadratic function as x increases?

• Remains constant

• Increases by consecutive odd numbers

• Decreases consistently

• Increases by the same amount each time

What happens to the y-value as x increases from 0 to 1 in the parent function?

• Remains the same

• Decreases by 1 unit

• Increases by 3 units

• Increases by 1 unit

What effect does the coefficient 3 have on the rate of change in the function y = 3x^2?

• It triples the rate of change

• It makes the graph wider

• It has no effect

• It reduces the rate of change

In the function y = 3x^2, how much does the y-value increase as x goes from 1 to 2?

• Increases by 9 units

• Increases by 12 units

• Increases by 3 units

• Decreases by 9 units

What is the vertex of the graph in the example discussed?

• (5, 7)

• (0, 0)

• (2, 4)

• (1, 3)

What is the axis of symmetry in the discussed example?

• x = 7

• y = 7

• x = 5

• y = 5

How does a negative coefficient affect the rate of change pattern?

• It has no effect

• It doubles the rate of change

• It reverses the direction of change

• It halves the rate of change

Why might the rate of change pattern not be useful for all quadratic equations?

• It only applies to linear functions

• It can be too complex to calculate

• Some quadratics do not have a clear vertex

• All options are correct

What alternative method is suggested for graphing when the rate of change pattern is not suitable?

• Using a graphing calculator

• Plugging values into the equation

• Estimating the graph shape

• Ignoring the vertex