Effects of 'a' on Quadratic Graphs

The video tutorial explores the quadratic function y = a * x^2, focusing on how the parameter 'a' affects the graph's shape. It explains that if 'a' is less than one, the graph becomes wider, while if 'a' is greater than one, it becomes narrower. A negative 'a' reflects the graph over the x-axis. The tutorial includes step-by-step graphing of y = 2x^2 and y = (1/3)x^2, demonstrating the effects of different 'a' values on the graph's width and direction.

What is the vertex of the basic quadratic function y = x^2?

• (0, 0)

• (2, 2)

• (1, 1)

• (0, 1)

How does the graph of y = a * x^2 change when 'a' is a fraction between 0 and 1?

• It becomes narrower.

• It becomes wider.

• It shifts upwards.

• It shifts downwards.

What happens to the graph of y = a * x^2 when 'a' is greater than 1?

• The graph becomes wider.

• The graph becomes narrower.

• The graph shifts to the left.

• The graph shifts to the right.

If 'a' is negative in y = a * x^2, what is the effect on the graph?

• The graph disappears.

• The graph opens downwards.

• The graph becomes a straight line.

• The graph opens upwards.

When 'a' is negative, what additional transformation occurs to the graph of y = a * x^2?

• It shifts to the right.

• It becomes a circle.

• It reflects over the x-axis.

• It shifts upwards.

What is the effect on the graph of y = a * x^2 when the absolute value of 'a' is between 0 and 1?

• The graph shifts to the right.

• The graph shifts to the left.

• The graph becomes wider.

• The graph becomes narrower.

In the example where a = 2, what is the y-coordinate when x = 2?

• 2

• 4

• 8

• 16

For a = 1/3, what is the y-coordinate when x = 3?

• -9

• -27

• -1

• -3

What is the effect on the graph of y = a * x^2 when 'a' is a fraction?

• The graph shifts upwards.

• The graph becomes wider.

• The graph shifts downwards.

• The graph becomes narrower.

In the graphing example, what is the y-coordinate for x = 1 when a = 2?

• 2

• 1

• 3

• 4