Quadratic Function Characteristics

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 does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards.

Front

How can you determine if a quadratic function has a maximum or minimum?

Back

If the coefficient of x² (a) is positive, the function has a minimum. If a is negative, the function has a maximum.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex 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 = h, where h is the x-coordinate of the vertex.

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 upwards?

Back

The range of a quadratic function that opens upwards is [k, ∞), where k is 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 (-∞, k], where k is the y-coordinate of the vertex.

Front

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

Back

The vertex (h, k) can be found using the formulas h = -b/(2a) and k = f(h), where f(h) is the value of the function at x = h.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.