Understanding Square Roots and Graphs

The video tutorial explains the concept of square roots, focusing on the principal square root, which is the positive square root of a number. It clarifies the notation and discusses the two square roots of a number, positive and negative. The tutorial then explores the graphs of the functions y = sqrt(x) and y = x^2, highlighting their relationships and transformations. It demonstrates how to graph these functions by hand and using a graphing calculator, and explains how to scale and shift these graphs. The tutorial concludes with a discussion on the symmetry of these functions and their transformations.

What does the principal square root of a number represent?

• The negative square root

• The square of the number

• The positive square root

• Both positive and negative square roots

How do you denote both the positive and negative square roots of a number?

• Using a multiplication sign

• Using a plus or minus sign

• Using a minus sign

• Using a plus sign

What happens to the x and y values when comparing y = x^2 and y = √x?

• They are swapped

• They are multiplied

• They are divided

• They remain the same

What is the symmetry line for the graphs of y = x^2 and y = √x?

• y = 0

• y = x

• x = y

• x = 0

How does scaling by a factor greater than 1 affect the graph of y = x^2?

• It shifts the parabola down

• It shifts the parabola up

• It makes the parabola narrower

• It makes the parabola wider

What effect does adding a constant to x^2 have on its graph?

• Shifts it right

• Shifts it up

• Shifts it down

• Shifts it left

How do you shift the graph of y = x^2 to the right?

• Subtract a constant from y

• Subtract a constant from x

• Add a constant to x

• Add a constant to y

What happens to the graph of y = √x when it is scaled by a factor less than 1?

• It shifts down

• It becomes narrower

• It becomes wider

• It shifts up

How do you shift the graph of y = √x to the left?

• Add a constant to x

• Subtract a constant from x

• Add a constant to y

• Subtract a constant from y

Why is it important to use the principal square root in graphing?

• To make the graph symmetrical

• To ensure the graph is a valid function

• To include negative values

• To simplify calculations