Recursive Equations and Quadratic Functions

The video tutorial explains how to write recursive equations for quadratic tables. It begins with identifying quadratic patterns by checking first and second differences. The instructor demonstrates writing recursive equations for two tables, emphasizing the need to express changing amounts in the equations. The video concludes with a summary and encouragement to practice.

What is the first step in writing recursive equations for quadratic tables?

• Check if the table is quadratic

• Identify the linear pattern

• Find the constant difference

• Determine the starting value

How can you confirm that a table represents a quadratic function?

• By verifying the values are decreasing

• By checking if the first difference is constant

• By ensuring the values are increasing

• By checking if the second difference is constant

What indicates that a table is not linear?

• The second difference is constant

• The first difference is constant

• The values are all even

• The first difference is not constant

What is the starting value for the recursive equation in Table A?

• f(0) = 0

• f(0) = 4

• f(0) = 2

• f(0) = 1

How do you determine the pattern for the recursive equation in Table A?

• By finding a constant number to add

• By identifying a linear pattern in the differences

• By subtracting the first value from the last

• By dividing each value by 2

What expression represents the changing amount in Table A?

• 2x + 1

• x + 2

• 2x - 1

• x - 2

How can you verify the recursive equation for Table A?

• By ensuring the equation is linear

• By checking if the first value matches

• By testing the equation with specific values

• By comparing it to a different table

What is the starting value for the recursive equation in Table B?

• f(0) = 0

• f(0) = 7

• f(0) = 14

• f(0) = 1

What expression represents the changing amount in Table B?

• 14x + 7

• 14x - 7

• 7x + 14

• 7x - 14

How do you verify the recursive equation for Table B?

• By comparing it to a different table

• By testing the equation with specific values

• By checking if the first value matches

• By ensuring the equation is linear