Transformations of Quadratic Functions Explained

What are the main types of transformations covered in this video?

• Translations, Reflections, and Rotations

• Translations, Rotations, and Dilations

• Translations, Reflections, and Shrinks/Stretches

• Reflections, Rotations, and Dilations

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

What does the 'K' value in the vertex form of a quadratic function represent?

• Vertical shift

• Horizontal stretch

• Vertical stretch

• Horizontal shift

If a quadratic function is given as G(x) = x^2 - 3, what transformation has occurred?

• Shifted left 3 units

• Shifted down 3 units

• Shifted up 3 units

• Shifted right 3 units

In the function G(x) = (x + 2)^2, what does the '+2' inside the parentheses indicate?

• Shifted 2 units down

• Shifted 2 units to the right

• Shifted 2 units up

• Shifted 2 units to the left

How do you identify if a function is vertically stretched or shrunk?

• By checking if the function has parentheses

• By looking at the coefficient of x

• By looking at the constant term

• By checking if the coefficient of x^2 is greater than or less than 1

What does a negative sign outside the parentheses in a quadratic function indicate?

• Reflection over the y-axis

• Reflection over the x-axis

• Horizontal shrink

• Vertical stretch

In the function G(x) = 3x^2, what type of transformation occurs?

• Vertical stretch by a factor of 3

• Vertical shrink by a factor of 3

• Horizontal stretch by a factor of 3

• Horizontal shrink by a factor of 3

For the function G(x) = (2x)^2, what is the transformation?

• Vertical stretch by a factor of 2

• Horizontal shrink by a factor of 1/2

• Vertical shrink by a factor of 2

• Horizontal stretch by a factor of 1/2

What is the transformation for G(x) = 1/5x^2 - 4?

• Vertical stretch by a factor of 1/5 and shifted up 4 units

• Vertical shrink by a factor of 1/5 and shifted down 4 units

• Horizontal stretch by a factor of 5 and shifted up 4 units

• Horizontal shrink by a factor of 5 and shifted down 4 units

In the function f(x) = 3(x + 2)^2 + 1, what transformations occur?

• Horizontal stretch by a factor of 3, shifted 2 units left, and 1 unit up

• Vertical stretch by a factor of 3, shifted 2 units left, and 1 unit up

• Horizontal shrink by a factor of 3, shifted 2 units right, and 1 unit down

• Vertical shrink by a factor of 3, shifted 2 units right, and 1 unit down