MA.7C Transformations of Quadratic Functions

Front

What is a transformation in the context of quadratic functions?

Back

A transformation refers to the changes made to the graph of a function, such as shifts, stretches, compressions, and reflections.

Front

What does a vertical shift of a quadratic function entail?

Back

A vertical shift moves the graph up or down without changing its shape. For example, adding a constant to the function shifts it up, while subtracting a constant shifts it down.

Front

How does a horizontal shift affect the graph of a quadratic function?

Back

A horizontal shift moves the graph left or right. Adding a constant inside the function shifts it left, while subtracting shifts it right.

Front

What is the effect of a reflection over the x-axis on a quadratic function?

Back

A reflection over the x-axis inverts the graph of the function, changing the sign of the output values.

Front

What does a vertical stretch of a quadratic function do?

Back

A vertical stretch increases the distance between points on the graph and the x-axis, making the graph narrower. This is achieved by multiplying the function by a factor greater than 1.

Front

What is a horizontal stretch in the context of quadratic functions?

Back

A horizontal stretch increases the distance between points on the graph and the y-axis, making the graph wider. This is achieved by multiplying the input variable by a factor less than 1.

Front

How can you identify a vertical shift in the equation of a quadratic function?

Back

A vertical shift can be identified by the constant added or subtracted from the function. For example, in the function f(x) = x^2 - 8, the -8 indicates a vertical shift down by 8 units.

Front

What does the equation k(x) = (x + 3)^2 - 2 represent in terms of transformations?

Back

This equation represents a horizontal shift 3 units to the left and a vertical shift 2 units down from the parent function f(x) = x^2.

Front

What is the significance of the coefficient in front of x^2 in a quadratic function?

Back

The coefficient affects the width and direction of the parabola. A positive coefficient opens upwards, while a negative coefficient opens downwards. The absolute value indicates the width.

Front

How does the transformation h(x) = -4x^2 differ from f(x) = x^2?

Back

The transformation h(x) = -4x^2 involves a reflection over the x-axis and a vertical stretch by a factor of 4.