Quadratic Functions - 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 parameter 'a' in a quadratic function affect?

Back

The parameter 'a' affects the width and direction of the parabola. If |a| > 1, the parabola is narrower; if 0 < |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 parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a) for the vertex's x-coordinate.

Front

How does the graph of f(x) = ax² transform when 'a' is negative?

Back

When 'a' is negative, the parabola opens downwards, indicating that the vertex is the maximum point of the function.

Front

What is the effect of adding a constant 'k' to a quadratic function, f(x) = ax² + k?

Back

Adding a constant 'k' vertically shifts the graph of the function up (if k > 0) or down (if k < 0) without changing its shape.

Front

What does it mean for a quadratic function to be 'wider' or 'narrower'?

Back

A 'wider' parabola has a smaller |a| value, indicating it stretches more horizontally. A 'narrower' parabola has a larger |a| value, indicating it stretches more vertically.

Front

What transformation does g(x) = f(x - 3) represent?

Back

The transformation g(x) = f(x - 3) represents a horizontal shift of the graph of f(x) to the right by 3 units.

Front

What transformation does g(x) = f(x + 2) represent?

Back

The transformation g(x) = f(x + 2) represents a horizontal shift of the graph of f(x) to the left by 2 units.

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).

Front

How does the graph of f(x) = ax² + bx + c change when 'b' is increased?

Back

Increasing 'b' affects the position of the vertex and the axis of symmetry, but does not change the width or direction of the parabola.