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 |a| < 1, it is wider. If a is positive, the parabola opens upwards; if negative, it 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. It can be found using the formula (-b/2a, f(-b/2a)).

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 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 the vertical shift of the graph. If k is positive, the graph shifts up; if negative, it shifts down.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k.

Front

How do you shift a quadratic function to the right by 2 units?

Back

To shift a quadratic function to the right by 2 units, replace x with (x - 2) in the function.

Front

What transformation does the equation y = 3(x - 3)² + 3 represent?

Back

This equation represents a vertical stretch by a factor of 3, a horizontal shift to the right by 3 units, and a vertical shift up by 3 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 + 4 shifts the graph up by 4 units.