Transformations of Quadratic Functions

This video tutorial covers the basics of quadratic functions and their transformations. It begins with an introduction to the parent function y = x^2 and explores how adding or subtracting constants affects the graph's vertical position. The tutorial then explains horizontal shifts caused by changes inside parentheses, reflections due to negative signs, and how coefficients affect the graph's width through stretching or compression. The video concludes with a summary and practical application of these transformations.

What is the vertex of the parent function y = x^2?

• (1, 1)

• (1, 0)

• (0, 0)

• (0, 1)

How does the graph of y = x^2 change when 3 is added to the function (y = x^2 + 3)?

• It shifts down by 3 units.

• It shifts up by 3 units.

• It shifts right by 3 units.

• It shifts left by 3 units.

What happens to the graph of y = x^2 when 4 is subtracted from the function (y = x^2 - 4)?

• It shifts down by 4 units.

• It shifts up by 4 units.

• It shifts left by 4 units.

• It shifts right by 4 units.

How does the graph of y = (x + 4)^2 differ from the parent function y = x^2?

• It shifts down by 4 units.

• It shifts left by 4 units.

• It shifts right by 4 units.

• It shifts up by 4 units.

What is the effect of subtracting 2 inside the parentheses in the function y = (x - 2)^2?

• It shifts right by 2 units.

• It shifts up by 2 units.

• It shifts down by 2 units.

• It shifts left by 2 units.

What transformation occurs when a negative sign is placed in front of the quadratic function (y = -x^2)?

• The graph reflects over the y-axis.

• The graph shifts down.

• The graph shifts up.

• The graph reflects over the x-axis.

How does the graph of y = 5x^2 compare to the parent function y = x^2?

• It becomes narrower.

• It becomes wider.

• It shifts up by 5 units.

• It shifts down by 5 units.

What happens to the graph of y = (1/2)x^2 compared to y = x^2?

• It becomes wider.

• It becomes narrower.

• It shifts down by 1/2 unit.

• It shifts up by 1/2 unit.

What is the term used to describe the transformation when a whole number is multiplied in front of x^2, making the graph narrower?

• Horizontal shift

• Vertical shift

• Vertical stretch

• Vertical compression

What is the term used to describe the transformation when a fraction is multiplied in front of x^2, making the graph wider?

• Horizontal shift

• Vertical shift

• Vertical stretch

• Vertical compression