Advanced Maths Assignment Semester Two: Linear Equations

Advanced Maths Assignment Semester Two

Linear

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. The common form of a linear equation is: y = mx + c. Displayed on a mathematical model, shows a straight line. The straight line represents a constant rise in numerical value, called the gradient, m. The y and x values indicate where on the mathematical model the line will be placed, and will always show a constant rise or decline ((1,1) (2,2)). The c value represents a constant number and indicates the equation will increase or decrease based on the value of the constant.

Polynomial

A polynomial is an expression that consists of variables and coefficients and only uses the operations addition, subtraction, multiplication and integers that are non-negative. In order to solves a polynomial, one must find the roots (Source 1.2) where the x value is 0 or when the polynomial line intersects with the x axis. Polynomials are used to construct algebraic varieties and polynomial rings and are used as central concepts in algebra and geometry.

Logarithmic

The logarithm of a number is the exponent to which the base must be raised to produce that number. The common form of a logarithm is b y = x ⇔ logb(x) = y. When creating a logarithmic

A quadratic equation will always have the form of a parabola when graphed; if a > 0 the parabola opens upwards whereas if a < 0 the parabola opens downwards. There are multiple ways to solves a quadratic, including factoring and completing the square to factorise the quadratic into the form (x + q) (x + s). In order to model a quadratic, one must find (h,k), the coordinates of the vertex. This can be done by rearranging ax2 + bx + c to a(x-h)2 + k where h = -b ÷ 2a and k = f(h) then one can plot the