Inverse Trig vs Reciprocal Trig Functions
Many students think that sin⁻¹(x) means 1/sin(x) but these expressions represent two completely different ideas. In this video, you’ll learn the difference between inverse trigonometric functions and reciprocal trigonometric functions. We’ll compare inverse sine, inverse cosine, and inverse tangent to cosecant, secant, and cotangent so you can avoid one of the most common mistakes in […]
Simplifying Complex Fractions Step-by-Step
Complex fractions can look intimidating, but they’re really just a combination of algebra skills you’ve already learned. In this video, you’ll learn how to simplify complex fractions involving rational expressions by combining expressions, multiplying by the reciprocal, factoring, and canceling common factors. We’ll work through an example step-by-step and show how multiple algebra concepts come […]
Transformations of Functions | a, h, and k Explained
Have you ever looked at the equationcand wondered what the values of a, h, and k actually do? In this video, we’ll start with the parent function and explore how each parameter changes the graph. You’ll learn how to recognize vertical stretches and compressions, horizontal shifts, and vertical shifts without memorizing complicated rules. In this […]
Who Created the Quadratic Formula?
Did someone actually create the quadratic formula, or does it come from somewhere else? In this lesson, we’ll start with the standard form of a quadratic equation and use the process of completing the square to derive the quadratic formula step by step. You’ll see that the quadratic formula isn’t magic and wasn’t simply invented […]
Determining the Angle of Elevation vs Angle of Depression
Understanding the difference between angles of elevation and angles of depression is an important application of right triangle trigonometry. In this lesson, you’ll learn how to identify each angle, draw accurate diagrams, and use them in trigonometric ratios to solve real-world problems involving heights, distances, and angles. Topics covered: • Angle of elevation • Angle […]
How Do We Determine End Behavior
Understanding end behavior is one of the most important skills when graphing polynomial functions. In this video, you’ll learn how to determine what happens to a polynomial as x approaches positive infinity and negative infinity. We’ll focus on how the degree of the polynomial and the sign of the leading coefficient work together to determine […]
Why Do Negative Exponents Switch Locations?
Negative exponents are often taught as a rule to memorize: move the base across the fraction bar and make the exponent positive. But why does that work? In this lesson, we use exponent patterns and the quotient rule to discover where negative exponents come from. By comparing exponent subtraction with expanded multiplication, you’ll see that […]
Why is there a ± for quadratics?
Why do we write ± when solving quadratic equations, but not when evaluating square roots? In this lesson, we’ll explore one of the most common misconceptions in algebra and uncover the reasoning behind it. You’ll learn how functions, inverses, and solving equations are connected, and why: ✔️ √25 = 5 ✔️ x² = 25 has […]
Rules of Exponents Explained
Exponent rules don’t have to be a collection of formulas to memorize. Once you understand the patterns behind exponents, the rules begin to make sense and become much easier to use. In this video, you’ll learn the most important exponent rules used throughout Algebra, Geometry, College Algebra, and ACT Math. We’ll work through examples and […]
Simplifying Square Roots Using Perfect Squares
Simplifying radicals doesn’t have to be complicated. The key is learning how to identify perfect square factors hidden inside the radical and use them to rewrite the expression in simplest form. In this video, you’ll learn a step-by-step method for simplifying square roots by breaking numbers into factors, finding the largest perfect square, and pulling […]