Transformations and Parent Functions

Front

What is a quadratic function?

Back

A polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does it mean to reflect a function over the x-axis?

Back

To reflect a function over the x-axis, you multiply the function by -1, changing the sign of the output values.

Front

How do you shift a function vertically?

Back

To shift a function vertically, you add or subtract a constant from the function. For example, f(x) + k shifts the graph up by k units, while f(x) - k shifts it down by k units.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x².

Front

What is an absolute value function?

Back

An absolute value function is a function that outputs the non-negative value of its input, typically in the form f(x) = |x|.

Front

How do you shift an absolute value graph horizontally?

Back

To shift an absolute value graph horizontally, you add or subtract a constant inside the absolute value. For example, f(x) = |x - k| shifts the graph right by k units, while f(x) = |x + k| shifts it left by k units.

Front

What is the effect of adding a constant to a quadratic function?

Back

Adding a constant to a quadratic function shifts the graph vertically. For example, f(x) = x² + k shifts the graph up by k units if k > 0 and down if k < 0.

Front

What is the effect of subtracting a constant from a quadratic function?

Back

Subtracting a constant from a quadratic function shifts the graph vertically down. For example, f(x) = x² - k shifts the graph down by k units.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

Front

What does it mean to shift a function to the right?

Back

Shifting a function to the right means to add a constant to the input variable. For example, f(x - k) shifts the graph right by k units.