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 is the vertex of a quadratic function?

Back

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

Front

What does it mean to translate a function vertically?

Back

Translating a function vertically means shifting the graph up or down along the y-axis. For example, f(x) + k shifts the graph up by k units if k > 0 and down by k units if k < 0.

Front

What does it mean to translate a function horizontally?

Back

Translating a function horizontally means shifting the graph left or right along the x-axis. For example, f(x - h) shifts the graph right by h units if h > 0 and left by h units if h < 0.

Front

What is a reflection in the context of quadratic functions?

Back

A reflection occurs when the graph of a function is flipped over a specific axis. For example, replacing f(x) with -f(x) reflects the graph across the x-axis.

Front

How does the value of 'a' in a quadratic function affect its graph?

Back

The value of 'a' determines the direction and width of the parabola. If a > 0, the parabola opens upwards; if a < 0, it opens downwards. A larger absolute value of 'a' makes the parabola narrower.

Front

What is the effect of adding a constant to a quadratic function?

Back

Adding a constant to a quadratic function, such as f(x) + k, results in a vertical translation of the graph. The graph shifts up by k units if k > 0 and down by k units if k < 0.

Front

What is the effect of subtracting a constant from the input of a quadratic function?

Back

Subtracting a constant from the input, such as f(x - h), results in a horizontal translation of the graph. The graph shifts right by h units if h > 0 and left by h units if h < 0.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

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, where (h, k) is the vertex of the parabola.