Transformations of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically 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 a quadratic function affect?

Back

The 'a' value affects the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

What is a vertical shift in a quadratic function?

Back

A vertical shift occurs when a constant is added or subtracted from the function, moving the graph up or down. For example, f(x) = x² + 3 shifts the graph up 3 units.

Front

What is a horizontal shift in a quadratic function?

Back

A horizontal shift occurs when the input variable x is adjusted by adding or subtracting a constant. For example, f(x) = (x - 2)² shifts the graph 2 units to the right.

Front

What is a reflection in the x-axis for a quadratic function?

Back

A reflection in the x-axis occurs when the 'a' value is negative, causing the parabola to open downward. For example, f(x) = -x² reflects the graph of f(x) = x².

Front

What is a vertical stretch in a quadratic function?

Back

A vertical stretch occurs when the 'a' value is greater than 1, making the parabola narrower. For example, f(x) = 2x² is a vertical stretch of f(x) = x².

Front

What is a vertical compression in a quadratic function?

Back

A vertical compression occurs when the 'a' value is between 0 and 1, making the parabola wider. For example, f(x) = 0.5x² is a vertical compression of f(x) = x².

Front

How do you identify a horizontal translation in a quadratic function?

Back

A horizontal translation is identified by changes in the x-value inside the function. For example, f(x) = (x + 3)² translates the graph 3 units to the left.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/2a.