Transforming 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.

Front

What does the 'a' value in a quadratic function affect?

Back

The 'a' value affects the width and direction of the parabola. If |a| > 1, the parabola is narrower; if 0 < |a| < 1, it is wider. If a < 0, the parabola opens downwards.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

How does the 'h' value in the vertex form of a quadratic function affect the graph?

Back

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

Back

The 'k' value represents a vertical shift. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the parent function of a quadratic function?

Back

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

Front

How do you determine if a quadratic function is a reflection over the x-axis?

Back

A quadratic function is reflected over the x-axis if the 'a' value is negative.

Front

What transformation occurs when you add a constant to a quadratic function?

Back

Adding a constant to a quadratic function results in a vertical shift. For example, f(x) = x² + 3 shifts the graph up by 3 units.

Front

What transformation occurs when you subtract a constant from a quadratic function?

Back

Subtracting a constant from a quadratic function results in a vertical shift down. For example, f(x) = x² - 2 shifts the graph down by 2 units.

Front

How do you shift a quadratic function to the right?

Back

To shift a quadratic function to the right, you subtract a positive constant from x in the function. For example, f(x) = (x - 2)² shifts the graph 2 units to the right.