Polynomial and Rational Functions

Polynomial Functions Pre-Calculus has a heavy emphasis on learning how to graph various functions. The Polynomial Functions Exploration is one strategy for learning how various functions behave based on the sign of their leading coefficient and the highest power of the polynomial. I find that my students remember functions ending behavior better when they discover [...]

By | 2017-11-13T22:01:56+00:00 September 2nd, 2016|PreCalculus|0 Comments

Graphing Polar Equations

We have spent some time learning how to graph circles, limacons, rose curves, and lemniscates on the polar coordinate plane. The material you see below is borrowed heavily from Yosh's Graphing Polar Equations part 1, part 2, and part 3. I have included a link to the Word document instead of a pdf of the [...]

By | 2017-11-13T22:01:56+00:00 April 26th, 2016|PreCalculus|0 Comments


The start of the second semester has me teaching both Algebra II and Pre-Calculus trigonometry simultaneously. My initial plan is to post material for both classes here. It it becomes confusing or too cumbersome, I'll split the two classes. Algebra II Right Triangle Trigonometry A foldable on trig concepts seems in order given the amount [...]

By | 2017-11-13T22:01:57+00:00 January 1st, 2016|Algebra II, PreCalculus|0 Comments

Systems of Equations and Inequalities

When you are given two lines, there are many ways to determine if and where they intersect. You can graph them, solve by substitution, solve by elimination, and use matrices to solve. Two-Variable Linear Systems Solving systems by elimination is the focus of this video. Two-Variable Linear Systems Section 7.2 notes Multi-Variable Linear Systems [...]

By | 2017-11-13T22:02:00+00:00 October 21st, 2015|PreCalculus|0 Comments

Solving Quadratic Equations

There are many ways to solve quadratic equations. The resources below can help you remember key concepts, discover new methods, and fine tune your skills. Solving by factoring and graphing is a worksheet that contains three types of equations - perfect square trinomials, difference of squares, and factoring trinomials to solve. It also has two solving [...]

By | 2017-11-13T22:02:00+00:00 September 25th, 2015|Algebra II, Algebra Tiles, PreCalculus|0 Comments

Quadratics Galore!

Graphing quadratic functions can be overwhelming. Not only are you working with translations and transformations, but a quadratic function can be written in three different forms. Follow the steps below and check your work using Desmos and you will be a pro in no time.     An accordion style foldable adapted from High Heels [...]

By | 2017-11-13T22:02:00+00:00 September 13th, 2015|Algebra II, PreCalculus|0 Comments

Combinations of Functions and Composite Functions

Composite functions are a combination of two functions. The traditional math course introduces them like this: Let f and g be functions with overlapping domains. Then for all x common to both domains: (f + g)(x) = f(x) + g(x) (f - g)(x) = f(x) - g(x) (fg)(x) = f(x) · g(x) (f/g)(x) = f(x) / [...]

By | 2017-11-13T22:02:00+00:00 August 26th, 2015|PreCalculus, Statistics|0 Comments

Graphical Symmetry

There are three types of graphical symmetry you may be responsible for: x-axis, y-axis, and origin. Knowing the properties of symmetry can help you when sketching complex graphs. x-Axis Symmetry If an equation or function is symmetric with respect to the x-axis. you can fold the paper it is graphed on along the x-Axis and [...]

By | 2017-11-13T22:02:00+00:00 August 16th, 2015|PreCalculus|0 Comments

Rectangular Coordinates

Coordinate Plane The coordinate plane is used to represent ordered pairs of real numbers by points in a plane and determine relationships between those points and the segments, lines or curves that connect them.   The axes form four quadrants. The x values are positive from the origin to the right and are negative from [...]

By | 2017-11-13T22:02:01+00:00 August 16th, 2015|PreCalculus|0 Comments