Graph Transformations of Quadratic Functions

The video tutorial explains how to graph the equation y = x^2 by choosing values for x and plotting the corresponding y values to form a parabola. It then demonstrates how to graph y = x^2 + 1 by shifting the original parabola up by one unit. The tutorial further explores how to graph equations of the form y = x^2 + n and y = x^2 - n by shifting the parabola up or down by n units. The video concludes with a summary of these graphing techniques.

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

• An ellipse

• A circle

• A parabola

• A straight line

If x = 2, what is the y-value for the equation y = x^2?

• 4

• 2

• 8

• 6

How does the graph of y = x^2 + 1 differ from y = x^2?

• It shifts to the left by 1 unit

• It shifts to the right by 1 unit

• It shifts upwards by 1 unit

• It shifts downwards by 1 unit

What is the y-value for x = 1 in the equation y = x^2 + 1?

• 1

• 2

• 4

• 3

What happens to the graph of y = x^2 if we change the equation to y = x^2 + 2?

• It moves up by 2 units

• It moves left by 2 units

• It moves down by 2 units

• It moves right by 2 units

If the equation is y = x^2 - 1, how does the graph change?

• It shifts left by 1 unit

• It shifts right by 1 unit

• It shifts up by 1 unit

• It shifts down by 1 unit

What is the vertex of the parabola for the equation y = x^2?

• (1, 0)

• (0, 1)

• (0, 0)

• (1, 1)

In the equation y = x^2 + 3, where is the vertex of the parabola located?

• (3, 0)

• (3, 3)

• (0, 3)

• (0, 0)

What is the effect of subtracting a constant from y = x^2?

• The graph shifts to the left

• The graph shifts to the right

• The graph shifts downwards

• The graph shifts upwards

What is the equation of the graph that is shifted 2 units upwards from y = x^2?

• y = x^2 - 1

• y = x^2 + 1

• y = x^2 - 2

• y = x^2 + 2