Complex Numbers and Quadratic Functions Review

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately. For example, (3 + 2i) + (4 - 5i) = (3 + 4) + (2i - 5i) = 7 - 3i.

Front

What is the square root of a negative number?

Back

The square root of a negative number is expressed in terms of the imaginary unit i. For example, √-36 = 6i.

Front

What is the axis of symmetry for a parabola?

Back

The axis of symmetry of a parabola is a vertical line that passes through the vertex. For a parabola with vertex (h, k), the axis of symmetry is x = h.

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 determine if a quadratic function has a maximum or minimum value?

Back

A quadratic function has a maximum value if it opens downwards (a < 0) and a minimum value if it opens upwards (a > 0).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots of the equation.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).