Graph Transformations and Effects

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. The tutorial also highlights the similarities between quadratic and absolute value graph transformations, emphasizing the role of parameters a, h, and k. Practical examples demonstrate how multiplying factors influence the graph's stretch or compression.

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

• Linear

• U-shaped

• V-shaped

• Circular

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

• It is V-shaped

• It is U-shaped

• It is a straight line

• It is a circle

What happens to the input values in a quadratic graph compared to an absolute value graph?

• They are doubled

• They are halved

• They are squared

• They remain the same

What are the parameters involved in transforming a quadratic graph?

• m, n, o

• a, h, k

• x, y, z

• a, b, c

How does the parameter 'h' affect the graph of a quadratic equation?

• Stretches it vertically

• Compresses it horizontally

• Shifts it up or down

• Shifts it left or right

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

• Right

• Down

• Up

• Left

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

• Shift upwards

• Shift downwards

• Shift to the left

• Shift to the right

What is the new vertex of the graph after shifting 4 units to the right and 5 units down?

• (-5, 4)

• (5, -4)

• (-4, 5)

• (4, -5)

How does the parameter 'a' affect the quadratic graph?

• It shifts the graph up or down

• It reflects the graph

• It shifts the graph left or right

• It stretches or compresses the graph horizontally

What happens to the graph when 'a' is less than 1?

• It stretches horizontally

• It compresses horizontally

• It shifts upwards

• It shifts downwards