Transformations of Quadratic Functions

The video tutorial explains how translations and shifts affect the graph of a parabola. It covers vertical shifts using G(x) = x^2 + 1 and H(x) = x^2 - 3, and horizontal shifts using J(x) = (x + 2)^2 and K(x) = (x - 1)^2. The tutorial emphasizes understanding the direction of shifts and common algebraic mistakes, providing a mnemonic: 'add to Y go high, add to X go west.'

What is the basic shape of the graph discussed in the introduction?

• Circle

• Parabola

• Ellipse

• Hyperbola

What happens to the graph of a function when a positive constant is added to it?

• It shifts to the right

• It shifts to the left

• It shifts upwards

• It shifts downwards

What happens to the graph of y = x^2 when y = x^2 + 1 is plotted?

• It shifts 1 unit right

• It shifts 1 unit up

• It shifts 1 unit down

• It shifts 1 unit left

What is the result of adding a constant to the y-value of a function?

• Horizontal shift

• Vertical shift

• No shift

• Reflection

What happens to the graph of y = x^2 when y = x^2 + 5 is plotted?

• It shifts 5 units up

• It shifts 5 units down

• It shifts 5 units left

• It shifts 5 units right

If a function is modified by subtracting a constant, what is the effect on its graph?

• The graph shifts to the right

• The graph shifts to the left

• The graph shifts downwards

• The graph shifts upwards

How does the graph of y = x^2 change when y = x^2 - 3 is plotted?

• It shifts 3 units down

• It shifts 3 units right

• It shifts 3 units left

• It shifts 3 units up

What is the result of subtracting a constant from the y-value of a function?

• Horizontal shift

• Vertical shift

• No shift

• Reflection

How does the graph of y = x^2 change when y = x^2 - 4 is plotted?

• It shifts 4 units up

• It shifts 4 units left

• It shifts 4 units right

• It shifts 4 units down

What is the effect of adding a constant to the x-value in a function?

• The graph shifts to the left

• The graph shifts downwards

• The graph shifts upwards

• The graph shifts to the right