Quadratic Functions Vocabulary

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 are the roots of a quadratic function?

Back

The roots of a quadratic function are the values of x for which the function equals zero. They are also known as solutions, x-intercepts, or zeros.

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 whether the parabola opens up or down.

Front

What does it mean for a parabola to open up?

Back

A parabola opens up when the coefficient of x² (a) is positive, indicating that the vertex is a minimum point.

Front

What does it mean for a parabola to open down?

Back

A parabola opens down when the coefficient of x² (a) is negative, indicating that the vertex is a maximum point.

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 domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, as there are no restrictions on the values that x can take.

Front

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

Back

The range of a quadratic function that opens up is from the y-coordinate of the vertex to positive infinity.

Front

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

Back

The range of a quadratic function that opens down is from negative infinity to the y-coordinate of the vertex.

Front

What is a maximum value in a quadratic function?

Back

The maximum value is the highest point on the graph of a quadratic function that opens down, occurring at the vertex.