Parabola Transformations and Properties

The video tutorial explains how to write equations for parabolas by examining shifts and transformations. It begins with the basic parabola equation and discusses how to identify horizontal and vertical shifts, vertical stretches, and flips. The tutorial includes four examples demonstrating these concepts, showing how to adjust the equation based on the parabola's transformations.

What is the basic equation of a parabola?

• y = 2x

• y = x^2

• y = x + 2

• y = x^3

Where is the vertex of the basic parabola located?

• At (0,0)

• At (1,1)

• At (2,2)

• At (-1,-1)

How does the parabola change if the vertex is shifted to the right?

• Divide x by 2

• Multiply x by 2

• Add to x

• Subtract from x

What happens to the equation if the parabola is shifted upwards?

• Add at the end

• Multiply by 2

• Subtract at the end

• Divide by 2

What indicates a vertical stretch in a parabola's equation?

• A negative sign

• A number less than 1 in front

• A number greater than 1 in front

• No change

In Example 1, how is the parabola shifted?

• Right 4, Down 3

• Left 4, Up 3

• Right 3, Down 4

• Left 3, Up 4

What is the equation for a parabola shifted right 4 units and down 3 units?

• y = (x - 3)^2 - 4

• y = (x - 4)^2 - 3

• y = (x + 3)^2 + 4

• y = (x + 4)^2 + 3

In Example 2, how is the parabola shifted?

• Right 2, Down 6

• Left 6, Up 2

• Right 6, Down 2

• Left 2, Up 6

What is the equation for a parabola shifted left 6 units and up 2 units?

• y = (x + 6)^2 + 2

• y = (x - 6)^2 - 2

• y = (x - 2)^2 - 6

• y = (x + 2)^2 + 6

In Example 3, what additional transformation is applied to the parabola?

• Shifted diagonally

• Compressed horizontally

• Stretched vertically

• Flipped upside down