Graph Transformations of Quadratic Functions

The video tutorial explains the characteristics and transformations of quadratic graphs, focusing on their U-shaped appearance compared to V-shaped absolute value graphs. It covers how transformations like shifting and stretching affect the graph's shape and position, and highlights the similarities between quadratic and absolute value graph transformations.

What is the basic shape of the graph of y = x^2?

• A straight line

• A U-shaped curve

• A circle

• A V-shaped curve

How does the graph of y = x^2 differ from the absolute value graph?

• It is a U-shaped curve

• It is a circle

• It is a straight line

• It is a V-shaped curve

What happens to the graph when you square the input values?

• It forms a U-shaped curve

• It becomes a circle

• It becomes a straight line

• It forms a V-shaped curve

What is the similarity between transformations of quadratic and absolute value graphs?

• They have different transformations

• They have the same transformations

• Quadratic graphs have more transformations

• Absolute value graphs have more transformations

What does the value of h represent in the transformation of a quadratic graph?

• Vertical shift

• Horizontal shift

• Reflection

• Stretching

If h is positive, in which direction does the graph shift?

• Down

• Left

• Right

• Up

What does a negative k value indicate in the transformation of a quadratic graph?

• Shift to the right

• Shift downwards

• Shift to the left

• Shift upwards

What is the new vertex if the graph is shifted 4 units right and 5 units down?

• (-5, 4)

• (5, -4)

• (-4, 5)

• (4, -5)

How does a coefficient of 1/2 affect the graph of y = x^2?

• It compresses the graph vertically

• It compresses the graph horizontally

• It stretches the graph vertically

• It stretches the graph horizontally

What effect does a whole number coefficient have on the graph?

• Compresses it horizontally

• Compresses it vertically

• Stretches it horizontally

• Stretches it vertically