Subtracting PolynomialsSubtract like terms by changing the signs of the terms being subtracted, and following the rules for adding polynomials. Below are several different ways to attack this example:Example 1: Subtract (2x2 + 4x – 6) from (x2 – 4) Solu…

Graphing ParabolasAn easy method for graphing parabolas involves preparing a chart. Of course, the graphing calculator can also be used for graphing. The graphs of quadratic functions, f (x) = ax2 + bx + c, are called parabolas.Shape of the Graph: Parab…

Powers of ProductsRule: For all numbers x and y , and integers n, “Notice: each factor of the product gets raised to the new power.” “Be sure to notice that this rule ONLY works when the inside of the parentheses is a single term (a product). ” “(no + s…

Straight Lines and SlopeThe slope of a line, m, is a rate of change which is constant in linear equations. When a line passes through the points (x1, y1) and (x2, y2), the slope, m, is expressed: Slopes may be positive, negative, zero, or undefined(doe…

Simplifying Radicals(For this lesson, the term “radical” will refer only to “square root”.) When working with the simplification of radicals you must remember some basic information about perfect square numbers. While there are certainly many more perfec…

Graphing Systems of InequalitiesIf you can graph an inequality, you can graph a system of inequalities!Simply graph each inequality separately on the same set of axes. The area where the shadings overlap is the solution to the system of inequalities. To…

FractionsFractions are used to represent parts of whole quantities. The denominator of a fraction (the bottom) shows the number of equal parts in the whole. The numerator of a fraction (the top) shows the number of parts being talked about or being used.…

ProportionsA proportion is a comparison of ratios.A proportion is an equation that states that two ratios are equal, such as Proportions always have an EQUAL sign!A proportion can be written in two ways: In each proportion the first and last terms (4 an…

Even and Odd Functions(1) Even function: If we put (–x) in place of x in the given function and if f(–x) = f(x), ∀ x ∈ domain then function f(x) is called even function. e.g. f(x) = ex + e-x , f(x) = x2, f(x) = x sin x, f(x) = cos x, f(x) = x2 cos x all …

How do you find the Minimum and Maximum Values of a Function?Maxima and Minima(1) A function f(x) is said to attain a maximum at x = a if there exists a neighbourhood (a – δ, a + δ) such that f(x) < f(a) for all x ∈ (a – δ, a + δ), x ≠ a ⇒ f(x) – f(a…