Characteristics of Quadratics

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upward or downward.

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 any real number can be input into the function.

Front

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

Back

The range 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 downward?

Back

The range is all real numbers less than or equal 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 downward.

Front

What is a minimum value in a quadratic function?

Back

The minimum value is the lowest point on the graph of a quadratic function that opens upward.

Front

How do you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting y = 0 and solving the equation ax² + bx + c = 0.