Quadratics - Graphing & Characteristics

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 shape does the graph of a quadratic function create?

Back

The graph of a quadratic function creates a U-shaped curve called a parabola.

Front

What is the vertex of a parabola?

Back

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

Front

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

Back

In vertex form, f(x) = a(x-h)² + k, the vertex is the point (h, k).

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

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

What is the range of a quadratic function that opens upwards?

Back

The range of a quadratic function that opens upwards is all real numbers greater than or equal to the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range of a quadratic function that opens downwards is all real numbers less than or equal to the y-coordinate of the vertex.

Front

What is a horizontal translation in the context of quadratic functions?

Back

A horizontal translation shifts the graph left or right. For example, f(x) = (x - 3)² translates the graph 3 units to the right.

Front

What is a vertical translation in the context of quadratic functions?

Back

A vertical translation shifts the graph up or down. For example, f(x) = x² + 4 translates the graph 4 units up.