Topic 8 Review

The graph of g(x) = ax² opens downward and is wider than the graph of f(x) = x². Which of the following could be the value of a?

• -10

• -0.1

• 0.1

• 10

The function f(x) = 2x² + x + 4 represents the number, in hundreds, of cups of coffee Fai expects to sell x weeks after opening his coffee shop. What is the average rate of change over the interval 2 ≤ x ≤ 4?

• -13

• 13

• 26

• 40

What is the point on the graph of function f(x) = 2(x - 4)² - 1 at x = 4?

• (4,-1)

• (4,-2)

• (4,1)

• (4,3)

What is the axis of symmetry of the function f(x) = -3x² + 12x - 11?

• x = -3

• x = -2

• x = 1

• x = 2

Over what interval is the function shown in the table increasing?

• x < 0

• x > 0

• -2 < x < 2

• all real numbers

What is the vertex of the graph of f(x) = (x + 1)² - 4?

• (-1, -4)

• (-1, 4)

• (1, -4)

• (1, 4)

The graph of h(x) = (x + 4)² - 7 is a transformation of the graph of f(x) = x². Complete the sentence. The graph of h is a translation ______ .

Suppose the function g(x) = -x²+ kx + 8 is a translation up 17 units and left 3 units of the parent function f(x) = -x². What is the value of k?

• A) k = -6

• B) k = -3

• C) k = 3

• D) k = 17

The function h(t) = -16t² + 18t models the height, in feet, of a jaguar t seconds after it jumps. What is the maximum height of the jump?

• A) 5 ft

• B) 6 ft

• C) 7 ft

• D) 8 ft

Part A: Joshua wants to surround a painting 16 inches by 20 inches with a frame that is x inches wide. Write a quadratic function A in standard form to represent the combined area of the painting and frame. A(x) = ______ x² + ______ x + ______.

Answer explanation