Shifts and Transformations of Parabolas

In this video, Ryan Malloy from the Worldwide Center of Mathematics explains how to shift a parabola. The tutorial covers both vertical and horizontal shifting. Vertical shifting involves adding or subtracting a constant to the equation, while horizontal shifting requires replacing x with x minus or plus a constant. The video provides examples and simplifications for better understanding.

What is the equation of the parabola discussed in the video?

• Y = x^2 - 2x + 3

• Y = x^2 + 2x - 3

• Y = x^2 + 3x - 2

• Y = x^2 - 3x + 2

What happens to the equation of a parabola when it is shifted vertically upwards by a units?

• Multiply the constant term by a

• Divide the constant term by a

• Add a to the constant term

• Subtract a from the constant term

If a parabola is shifted downwards by 3 units, what change is made to its equation?

• Add 3 to the constant term

• Subtract 3 from the constant term

• Multiply the constant term by 3

• Divide the constant term by 3

What is the general effect of adding a constant to the y variable in a parabola's equation?

• Stretches the parabola

• Shifts the parabola horizontally

• Compresses the parabola

• Shifts the parabola vertically

What is the effect of subtracting a constant from the y variable in a parabola's equation?

• Shifts the parabola to the left

• Shifts the parabola to the right

• Shifts the parabola downwards

• Shifts the parabola upwards

To shift a parabola to the right by 2 units, what substitution is made in the equation?

• Replace x with x + 2

• Replace x with x - 2

• Replace x with 2x

• Replace x with -2x

What is the result of shifting the parabola y = x^2 + 2x - 3 one unit to the right?

• y = (x - 1)^2 - 2(x - 1) + 3

• y = (x + 1)^2 - 2(x + 1) + 3

• y = (x - 1)^2 + 2(x - 1) - 3

• y = (x + 1)^2 + 2(x + 1) - 3

What is the simplified form of the equation after shifting y = x^2 + 2x - 3 one unit to the right?

• y = x^2 + 4

• y = x^2 - 2

• y = x^2 - 4

• y = x^2 + 2

What is the effect of subtracting a constant from the x variable in a parabola's equation?

• Shifts the parabola upwards

• Shifts the parabola to the right

• Shifts the parabola to the left

• Shifts the parabola downwards

What is the effect of replacing x with x - b in the equation of a parabola?

• Shifts the parabola to the right by b units

• Shifts the parabola to the left by b units

• Shifts the parabola upwards by b units

• Shifts the parabola downwards by b units