Quadratic Transformations

Front

What is the vertex form of a quadratic function?

Back

f(x) = a(x-h)² + k

Front

What does the 'a' in the vertex form f(x) = a(x-h)² + k represent?

Back

The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

How does changing 'h' in the vertex form f(x) = a(x-h)² + k affect the graph?

Back

Changing 'h' shifts the graph horizontally. If 'h' increases, the graph shifts to the right; if 'h' decreases, it shifts to the left.

Front

What effect does changing 'k' in the vertex form f(x) = a(x-h)² + k have on the graph?

Back

Changing 'k' shifts the graph vertically. If 'k' increases, the graph shifts up; if 'k' decreases, it shifts down.

Front

What transformation occurs when a quadratic function is reflected across the x-axis?

Back

The 'a' value in the vertex form becomes negative, causing the parabola to open downwards.

Front

Describe the transformation of y = f(x) to y = f(x) + c where c > 0.

Back

The graph of y = f(x) is shifted up by 'c' units.

Front

Describe the transformation of y = f(x) to y = f(x) - c where c > 0.

Back

The graph of y = f(x) is shifted down by 'c' units.

Front

What does it mean to compress a quadratic function vertically?

Back

A vertical compression occurs when the absolute value of 'a' in the vertex form is less than 1, making the parabola wider.

Front

What does it mean to stretch a quadratic function vertically?

Back

A vertical stretch occurs when the absolute value of 'a' in the vertex form is greater than 1, making the parabola narrower.

Front

How do you represent a horizontal shift to the right in a quadratic function?

Back

To shift a function to the right by 'h' units, replace 'x' with 'x-h' in the function.