Graph Transformations and Quadratic Functions

This video tutorial explains how to graph the quadratic equation y = x^2 and demonstrates how to perform vertical and horizontal translations on the graph. It covers moving the graph up, down, left, and right by adjusting the equation, and explains the reasoning behind these transformations. The video also addresses common misconceptions and provides examples to clarify the concepts.

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

• A parabola

• A straight line

• An ellipse

• A circle

If x = 3, what is the value of y in the equation y = x^2?

• 3

• 12

• 9

• 6

What happens to the graph of y = x^2 when you add 3 to the equation?

• It shifts 3 units upwards

• It shifts 3 units to the left

• It shifts 3 units downwards

• It shifts 3 units to the right

How do you modify the equation y = x^2 to move the graph down 3 units?

• Divide x^2 by 3

• Multiply x^2 by 3

• Subtract 3 from x^2

• Add 3 to x^2

What is the effect of replacing x with x + 3 in the equation y = x^2?

• The graph moves 3 units downwards

• The graph moves 3 units to the left

• The graph moves 3 units to the right

• The graph moves 3 units upwards