What is a dialation for a quadratic graph

The video tutorial explains the concept of dilation in mathematics, focusing on how it affects linear and quadratic graphs. It begins with an introduction to dilation using linear graphs, explaining how multiplying by a factor changes the slope. The tutorial then explores dilation in quadratic functions, demonstrating how different factors affect the graph's shape. The effects of dilation, such as horizontal stretching and compression, are analyzed. Finally, the video covers the rules for determining dilation effects using the vertex form of a quadratic equation.

What happens to the graph of y = x when it is multiplied by 1/2?

• The graph shifts upwards.

• The graph becomes steeper.

• The graph becomes less steep.

• The graph shifts downwards.

In the context of quadratic functions, what is the starting point of the identity function y = x^2?

• (1, 1)

• (2, 4)

• (0, 0)

• (0, 1)

How does multiplying y = x^2 by 1/2 affect the graph?

• It shifts the graph to the right.

• It stretches the graph horizontally.

• It shifts the graph to the left.

• It compresses the graph vertically.

What is the effect of multiplying y = x^2 by 2?

• The graph is shifted upwards.

• The graph is stretched horizontally.

• The graph is compressed horizontally.

• The graph is shifted downwards.

In the vertex form y = a(x - h)^2 + k, what does the value of 'a' determine?

• The axis of symmetry.

• The horizontal shift of the graph.

• The vertical shift of the graph.

• Whether the graph is stretched or compressed.

What happens if the absolute value of 'a' is less than 1 in a quadratic function?

• The graph is shifted downwards.

• The graph is shifted upwards.

• The graph is stretched horizontally.

• The graph is compressed horizontally.

If the absolute value of 'a' is greater than 1, what is the effect on the graph?

• The graph is compressed horizontally.

• The graph is shifted to the left.

• The graph is stretched horizontally.

• The graph is shifted to the right.