Quadratic Functions

• A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.

Parabloa

• The parabola is the curve formed from all the points (x, y)
• The line in the middle that splits it is the axis of symmetry

Axis of Symmetry

• The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves
• The axis of symmetry always passes through the vertex of the parabola.

Quadratic Equations

• A quadratic equation is a second-order polynomial equation in a single variable.
• Each quadratic equation has 2 solutions.
• solutions may be both real, or both complex.

Standard Form of Quadratic

• a function that can be written in the form f(x) = ax2 + bx + c where a, b, and c are real numbers and a = 0. Parabola
• The graph of a squaring function is called a parabola. It is a U-shaped graph

Vertex Form of Quadratic

• To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square.
• the vertex of the parabola

Zero Product Property

• states that the product of two nonzero elements is nonzero. In other words, it is the following assertion: If , then oralso known as the rule of zero product

Zeros of Function

• Zeros of Function is an input value that produces an output of zero
• If the function maps real numbers to real numbers, its zeroes are the x-coordinates of the points where its graph meets the x-axis

Factoring

• the process of finding the factors
• Finding what to multiply together to get an expression
• also known as "splitting"

Difference of Two Squares

• An algebraic term is a perfect square when the numerical coefficient (the number in front of the variables) is a perfect square and the exponents of each of the variables are even numbers

Perfect Square Trinomials

• A trinomial can be a perfect square
• 3 monomials

Quadratic Formula

• Quadratic Formula can always find the solution
• The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you to solve.

Discriminant

• The discriminant is the name given to the expression that appears under the square root (radical) sign in the quadratic formula
• Discriminant. The discriminant tells you about the "nature" of the roots of a quadratic equation given that a, b and c are rational numbers.

Imaginary Number

• a complex number that can be written as a real number multiplied by the imaginary unit i,
• defined by its property i2 = −1. The square of an imaginary number bi is −b2.
• For example, 6i is an imaginary number, and its square is −36.

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

Quadratic Functions