The graph of the function y = x² is shown below.

How will the graph be affected if the coefficient of x is increased to 4?

A. The parabola will be translated up.
Incorrect. Increasing the coefficient of x does not move the parabola.

B. The parabola will be translated down.
Incorrect. Increasing the coefficient of x does not move the parabola.

C. The parabola will be wider.
Incorrect. Increasing the coefficient of x will not make the parabola wider.

D. The parabola will be narrower.
Correct! Increasing the coefficient of x will make the parabola narrower.

What is the effect on the graph of the equation y = 3x² when the equation is changed to y = -3x²?

A. The graph of y = -3x² is a reflection of y = 3x² across the x-axis.
Correct! Changing the value of the coefficient from 3 to -3 will reflect the graph across the x-axis.

B. The graph of y = -3x² is a reflection of y = 3x² across the y-axis.
Incorrect. The graph will be reflected across the x-axis.

C. The graph of y = -3x² is translated 6 units up.
Incorrect. Changing the coefficient of the x does not translate the graph.

D. The graph of y = -3x² is translated 6 units down.
Incorrect. Changing the coefficient of the x does not translate the graph.

Which shows the functions correctly listed in order from widest to narrowest graph?

1. y = 9 4 x², y = 2x², y = 5 4x², y = 1 2x²
2. y = 1 2x², y = 5 4x², y = 2x², y = 9 4 x²
3. y = 9 4 x², y = 5 4x², y = 2x², y = 1 2x²
4. y = 2x², y = 1 2x², y = 5 4x², y = 9 4 x²

A.
Incorrect. This order is from narrowest to widest graph.

B.
Correct! These functions are correctly listed in order from widest to narrowest graph.

C.
Incorrect. The widest graph will be y = 1/2x².

D.
Incorrect. The widest graph will be y = 1/2x².

The graphs below represent functions of the form y = ax². In which of the following graphs does a appear to have the smallest value?

A.	C.
B.	D.

A.
Correct! Since this is the widest parabola, the value of a must be the smallest.

B.
Incorrect. You are looking for the graph that is the widest.

C.
Incorrect. You are looking for the graph that is the widest.

D.
Incorrect. You are looking for the graph that is the widest.