Quadratic Functions and Differences

This video reviews writing explicit equations for simpler quadratic functions, focusing on those without a middle x term. It explains how to find first and second differences, derive the quadratic equation, and verify it through examples. The video also covers finding the constant term when the x value is zero, emphasizing the form ax^2 plus C.

What is the form of the simpler quadratic functions discussed in the video?

• ax^2 + bx + c

• ax^2 + c

• ax + b

• ax^2 + bx

What is the first step in finding the first and second differences?

• Subtracting the x values

• Extending the table to the right

• Adding a new row

• Multiplying the differences

How do you calculate the second differences?

• By adding the first differences

• By subtracting the first differences

• By dividing the first differences

• By multiplying the first differences

What is the relationship between the second difference and the coefficient of x^2?

• The coefficient is double the second difference

• The coefficient is half the second difference

• The coefficient is equal to the second difference

• The coefficient is the square of the second difference

What form does the function take if the second difference is -4?

• f(x) = -4x^2

• f(x) = -2x^2

• f(x) = 4x^2

• f(x) = 2x^2

What should be added to the function f(x) = -2x^2 to make it correct?

• Add 8

• Add 5

• Add 6

• Add 7

How can you verify the correctness of the quadratic function?

• By checking with one value

• By checking with two values

• By checking with four values

• By checking with three values

What is the first step in the second example of finding a quadratic function?

• Adding a new row

• Extending the table to the right

• Subtracting the x values

• Multiplying the differences

What is the second difference in the second example?

• 20

• 15

• 10

• 5

What is the coefficient of x^2 in the second example?

• 2.5

• 10

• 5

• 7.5