Key Features of 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 and a ≠ 0.

Front

What shape does the graph of a quadratic function take?

Back

The graph of a quadratic function is called a parabola.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on the direction 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 minimum value of a quadratic function?

Back

The minimum value occurs at the vertex of the parabola when it opens upwards (a > 0).

Front

What is the maximum value of a quadratic function?

Back

The maximum value occurs at the vertex of the parabola when it opens downwards (a < 0).

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept is found by evaluating the function at x = 0, which gives the point (0, c) in the function f(x) = ax² + bx + c.

Front

What does it mean for a quadratic function to be increasing?

Back

A quadratic function is increasing on the interval where the x-values are greater than the x-coordinate of the vertex if the parabola opens upwards.

Front

What does it mean for a quadratic function to be decreasing?

Back

A quadratic function is decreasing on the interval where the x-values are less than the x-coordinate of the vertex if the parabola opens upwards.

Front

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

Back

The range is all real numbers greater than or equal to the y-coordinate of the vertex.