Characteristics of Quadratic Functions

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 is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

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 from the vertex form of a quadratic function?

Back

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

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0).

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' in the standard form f(x) = ax² + bx + c is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

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 formula x = -b/(2a).

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex; it is the y-coordinate of the vertex.

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 minimum value.

Front

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

Back

The range is all real numbers less than or equal to the maximum value.