A1 Introduction to Quadratic Functions

Lily earns the same amount of money each week from her part-time job. What type of function produces a constant difference between consecutive output values, like Lily's weekly earnings?

• Exponential function

• Quadratic function

• Linear function

• Absolute value function

Avery is tracking the height of a ball thrown upward at regular time intervals. Which of the following describes how the height changes as each second passes?

• The height increases by a constant amount

• The height is multiplied by a constant factor

• The second differences of the height values are constant

• The height decreases by a constant amount

Henry is building a sequence of square-shaped gardens. The first garden has 1 square, the second garden has 4 squares, the third garden has 9 squares. Which function represents the number of squares in the nth garden?

• f(n) = 2n

• f(n) = n^2

• f(n) = 2^n

• f(n) = n + 3

Arjun is decorating a square table by adding border tiles around its edge. If the inner square table has side length n, which expression represents the number of border tiles Arjun adds?

• 4n

• 4n + 4

• n^2 + 4

• 2n + 2

Olivia is arranging a pattern of dots so that the n-th figure has n^2 + 2n dots. How many dots are in the 5th figure?

• 30

• 35

• 25

• 27

Emma is arranging tiles in a geometric pattern. She notices that the total number of tiles after each step is: 3, 8, 15, 24. Determine the quadratic function f(n) that models the total number of tiles Emma uses at step n.

• f(n) = n^2 + n + 1

• f(n) = n^2 + 2n

• f(n) = 2n^2 - 1

• f(n) = n^2 + n - 1

Liam invests in two different savings accounts. In the first account, the amount grows according to f(x) = x^2, where x is the number of years. In the second account, the amount grows according to g(x) = 2^x. Which of the following statements is true when comparing the growth of these two accounts for large values of x?

• f(x) grows faster than g(x)

• g(x) grows faster than f(x)

• Both functions grow at the same rate

• f(x) is always greater than g(x)

Scarlett is comparing two ways to grow her savings. One way grows her money by squaring the amount each year (f(x) = x^2), and the other doubles it each year (g(x) = 2^x). At year x = 2, which method gives her more money?

• f(x) = x^2 is greater

• g(x) = 2^x is greater

• They are equal

• Cannot be determined

Olivia is comparing two ways to grow her savings: one grows quadratically, f(x) = x^2, and the other grows exponentially, g(x) = 3^x. For which value of x does Olivia's exponentially growing savings first exceed her quadratically growing savings for x > 0?

• x = 1

• x = 2

• x = 3

• x = 4

A ball is thrown upward and its height in feet is modeled by h(t) = -16t^2 + 64t + 5. What does the constant term 5 represent in this context?

• The maximum height of the ball

• The time it takes to reach the maximum height

• The initial height of the ball when t = 0

• The speed at which the ball is thrown