Honors Math 2: 5.1-5.3 Review

Flashcards covering key concepts from Honors Math 2, including solving quadratic equations using various methods, complex numbers, vertex form, and the discriminant.

Square Root Property

A method to solve quadratic equations of the form x^2 = c or (ax+b)^2 = c, where the solution is x = ±√c or ax+b = ±√c.

Complex Number

A number that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit.

Imaginary Unit (i)

Defined as the square root of -1 (√-1), meaning i^2 = -1.

Addition and Subtraction of Complex Numbers

Performed by combining the real parts and the imaginary parts separately: (a + bi) ± (c + di) = (a ± c) + (b ± d)i.

Multiplication of Complex Numbers

Performed by applying the distributive property (FOIL) and substituting i^2 with -1.

Division of Complex Numbers

Achieved by multiplying the numerator and denominator by the complex conjugate of the denominator to eliminate the imaginary part from the denominator.

Completing the Square

A method used to solve quadratic equations by manipulating the equation to create a perfect square trinomial on one side.

Vertex Form of a Quadratic Equation

The form y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola, indicating the maximum or minimum value of the quadratic function.

Quadratic Formula

Used to find the solutions (roots) of a quadratic equation in the form ax^2 + bx + c = 0, given by x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Discriminant

The expression b^2 - 4ac found within the quadratic formula, which determines the nature of the roots of a quadratic equation.

Nature of Roots (Discriminant > 0)

If the discriminant (b^2 - 4ac) is greater than zero, there are two distinct real solutions/roots.

Nature of Roots (Discriminant = 0)

If the discriminant (b^2 - 4ac) is equal to zero, there is exactly one real solution/root (a repeated real root).

Nature of Roots (Discriminant < 0)

If the discriminant (b^2 - 4ac) is less than zero, there are two imaginary (non-real) solutions/roots, which are complex conjugates.