Transformations - Quadratic Functions

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.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, given by the coordinates (h, k) in the vertex form f(x) = a(x - h)² + k.

Front

What does the 'a' value in the vertex form f(x) = a(x - h)² + k indicate?

Back

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

Front

How does a vertical shift affect a quadratic function?

Back

A vertical shift moves the graph of the function up or down without changing its shape. This is represented by the 'k' value in the vertex form.

Front

What is the effect of a horizontal shift on a quadratic function?

Back

A horizontal shift moves the graph of the function left or right, determined by the 'h' value in the vertex form.

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

How do you find the vertex from the standard form of a quadratic function?

Back

The vertex can be found using the formula h = -b/(2a) and k = f(h).

Front

What does it mean for a quadratic function to be in vertex form?

Back

A quadratic function is in vertex form when it is expressed as f(x) = a(x - h)² + k, making it easy to identify the vertex (h, k).

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 = h, where (h, k) is the vertex.

Front

What happens to the graph of a quadratic function when 'a' is negative?

Back

When 'a' is negative, the parabola opens downward, and the vertex represents the maximum point of the function.