How to Solve (and Factor) a Quadratic Equation with the Quadratic Formula
A quadratic equation is any second-degree polynomial equation — that’s when the highest power of x,or whatever other variable is used, is 2. The solution or solutions of a quadratic equation, [more…]
How to Solve a Quadratic Equation by Completing the Square
You can solve quadratic equations by completing the square. Completing the square involves creating a perfect square trinomial from the quadratic equation, and then solving that trinomial by taking its [more…]
How to Solve (and Factor) a Quadratic Equation with the Quadratic Formula
A quadratic equation is any second-degree polynomial equation — that’s when the highest power of x,or whatever other variable is used, is 2. The solution or solutions of a quadratic equation, [more…]
How to Express Exponential Relationships with Logarithms
You may come across logarithms in your calculus work. A logarithm is just a different way of expressing an exponential relationship between numbers. For instance, [more…]
How to Simplify Roots
When you work with roots in an equation, you often need to simplify them. There are two methods: the quick, sort of intuitive method, and a slightly longer method. The quick method of simplification works [more…]
How to Factor Mathematical Expressions
You often need to factor expressions (break those expressions into their simpler components, or factors) for calculus. Factoring means “unmultiplying,” like rewriting 12 as [more…]
Understanding the Properties of Numbers
Remembering the properties of numbers is important because you use them consistently in pre-calculus. The properties aren’t often used by name in pre-calculus, but you’re supposed to know when you need [more…]
How to Graph Linear Inequalities
You can use the slope-intercept form to graph inequalities. The slope-intercept form is expressed as y = mx + b, where the variable m stands for the slope of the line, and [more…]
Comparing Radicals and Exponents
Radicals and exponents (also known as roots and powers) are two common — and oftentimes frustrating — elements of basic algebra. And of course they follow you wherever you go in math, just like a cloud [more…]
How to Rewrite Radicals as Exponents
When you’re given a problem in radical form, you may have an easier time if you rewrite it by using rational exponents— exponents that are fractions. You can rewrite every radical as an exponent by using [more…]
How to Rationalize a Radical Out of a Denominator
A convention of mathematics is that you don’t leave radicals in the denominator of an expression when you write it in its final form. Thus we do something called [more…]
How to Express Solutions for Inequalities with Interval Notation
You can use interval notation to express where a set of solutions begins and where it ends. Interval notation is a common way to express the solution set to an inequality, and it’s important because it’s [more…]
How to Perform Operations with Complex Numbers
Sometimes you come across situations where you need to operate on real and imaginary numbers together, so you want to write both numbers as complex numbers in order to be able to add, subtract, multiply [more…]
How to Solve Inequalities Containing Absolute Values
An absolute-value equation usually has two possible solutions. Absolute value is a bit trickier to handle when you’re solving inequalities. The two possible solutions are: [more…]
