Topic 8 - Quadratic Functions

Adam graphs f(x) = x² and g(x) = 3x². Which of the following is NOT the same for the graphs of functions f and g ?

• location of the vertex

• axis of symmetry

• y -value when x = 5

• direction parabola opens

Match each graph with its function.

• h(x) = 0.5x²

• 
• j(x) = 2x²

• 
• f(x) = -2x²

• 
• g(x) = -x²

• 

For which function is the average rate of change over the

interval 1 < x < 5 greater than the average rate of change

over the same interval for the function g(x) = 1.8x² ?

• f(x) = x²

• g(x) = 1.2x²

• h(x) = 1.5x²

• k(x) = 2x²

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

• x < -2

• x < 0

• x > 0

• x < 2

How does the graph of f(x) = x² + 2 compare to the graph of g(x) = x² + 8 ?

The graph of g(x) is the graph of f(x) shifted ​ (a)   units ​ (b)   .

• 6
• up
• 2
• 8
• down
• left
• right
• 10

What is the vertex of the graph of f(x) = (x + 8)² − 3 ?

• (-8, 3)

• (8, 3)

• (8, -3)

• (-8, -3)

What is an equation for the quadratic function represented by the table shown?

g(x) = ​ (a)   (x - ​ (b)   )² + ​ (c)  

• -1
• 2
• 3
• 1
• -2

The graph of function g is a parabola with the vertex located at (5, 9) . The parabola also passes through the points (7, 1) and (3, 1) . Select an equation in vertex form for the function.

• g(x) = 2(x − 5)² + 9

• g(x) = 2(x − 5)² − 9

• g(x) = − 2(x − 5)² + 9

• g(x) = − 2(x + 5)² + 9

What is the vertex of the graph of f(x) = x² + 4x + 6 ?

• (-4, 6)

• (-2, 2)

• (2, -2)

• (3, 27)

A ball is thrown into the air. The function h(x) = −16x² + 64x + 8 models the height, in feet above ground, of the ball after x seconds.

What was the height of the ball at the time it was thrown? ​ (a)   feet above ground.

How many seconds after being thrown did the ball reach its maximum height? ​ (b)   seconds.

• 8
• 2
• 0.5
• 1
• -4