Quadratic Transformations

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

The 'a' value represents the vertical stretch or compression of the graph. If |a| > 1, the graph is narrower; if 0 < |a| < 1, the graph is wider.

Front

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

Back

Changing 'h' shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, 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 is positive, the graph shifts up; if k is negative, it shifts down.

Front

How does the graph of y = x² change when it is reflected over the x-axis?

Back

The graph of y = x² becomes y = -x², which opens downward instead of upward.

Front

What transformation occurs when the graph of y = x² is shifted up 4 units?

Back

The new equation becomes y = x² + 4.

Front

What transformation occurs when the graph of y = x² is shifted down 4 units?

Back

The new equation becomes y = x² - 4.

Front

What transformation occurs when the graph of y = x² is shifted left 4 units?

Back

The new equation becomes y = (x + 4)².

Front

What transformation occurs when the graph of y = x² is shifted right 4 units?

Back

The new equation becomes y = (x - 4)².

Front

What does a vertical compression of a quadratic function look like?

Back

A vertical compression makes the graph wider. For example, f(x) = (1/2)x² is a vertical compression of f(x) = x².