Understanding Quadratic Functions

The function f(x) = x^2 - 2x. Which statement is true about the graph of f?

• The graph has a y-intercept at (2, 0)

• The coordinates of the vertex are (1,1)

• The graph of the function opens downward.

• The x-intercepts are at (0, 0) and (2, 0).

A quadratic function f is given by f(x) = ax^2 + bx + c where a is not 0. Select all the statements that must be true about the graph of f.

• The y-intercept of the graph is at (0, c).

• The graph has an x-intercept at (c, 0)

• When a < 0 the graph opens downward.

• The graph has two x-intercepts.

• If b = 0, then the vertex is on the y-axis.

What are the x-intercepts of the quadratic function p(x) = (x - 1)(x + 3)?

• -3 and 1

• 1 and 3

• -1 and 3

• -3 and -1

Fill in the blank: The vertex of the quadratic function p(x) = (x - 1)(x + 3) is at the point ____.

• A) (1, -4)

• B) (-1, -4)

• C) (2, 0)

• D) (-2, -4)

Whose stone hit the water first? Use the graph to determine the answer.

• Clare's

• Lin's

The function f(t) = (-16t - 8)(t - 1) represents the height of a stone t seconds after it was thrown by Clare. How many seconds after the stone was tossed did it hit the water? Fill in the blank: The stone hit the water after ____ seconds.

• 1

• 1.5

• 2

• Graph A

• Graph B

• Graph C

• Graph D

If you were to shift the graph of y = x^2 - x - 6 6 units down from where it is now, what would be the equation represented by the new graph?

• y = x^2 - x - 12

• y = x^2 - x - 0

• y = x^2 - x - 6

• y = x^2 - x - 18

The graph shows the function y = g(x), where g(x) represents a transformation of f(x) = x^2. What is the equation for g(x)?

• g(x) = (x - 2)^2 - 1

• g(x) = (x + 2)^2 - 1

• g(x) = -(x - 2)^2 + 1

• g(x) = -(x + 2)^2 + 1

What is the correct answer for question 1?

• A) A

• B) B

• C) C

• D) D