Author Archives: admin
Maximum & Minimum Word Problems
Sometimes teachers give you word problems based on parabolas, where they're asking you to maximize area of a picture frame or cattle pen, or minimize the product of a pair of numbers. These are their stories.
The Discriminant of a Parabola
This is a simple topic that teachers nonetheless find a way to make confusing (based on the number of questions I get about it). In this video I'll show you what the discriminant is, how to find it, and how to get this question right on the test.
Finding the Roots of a Parabola
"Roots", "zeros", "solutions" and "x-intercepts" of a quadratic all mean the same thing: the answers you get when you set a parabola equation equal to 0 and solve. In this video, we'll practice finding these and using them to graph parabolas.
Parabolas -- Vertex Form Graphing & Vocab
In this video we get at the basics of graphing quadratic functions (parabolas) that are already in vertex form: axis of symmetry, domain, range, orientation, maximum/minimum, and intervals of increasing/decreasing. (For more on finding x-intercepts/zeros of quadratics, check out my solving quadratics chapter.)
How to put quadratics in "vertex form"
In this video I cover how to find all the same parabola stuff as last video -- vertex, axis of symmetry -- but for harder problems when the equation isn't already in vertex form, either by completing the square or using the "-b/2a trick". (For more on completing the square, check out my solving quadratics chapter.)
Graphing Logs vs Exponentials (free)
This is the biggest confusion my tutoring students have with Logs & Exponentials -- telling log graphs apart from exponential graphs, and knowing how to graph each -- so this video will probably help you too! (Hint: it will involve vertical asymptotes and horizontal asymptotes, and which goes with what.)
Graphing Logs
Let's face it, graphing logs is a dog. The worst. But to conquer these beasts you must simply never forget, ever ever, that logs always and only have vertical asymptotes. (awkward silence) We get into some other transformation stuff too.
Solving Difficult Log Equations
At the end of each problem we'll do the "curly q" we'd use to solve an equation with only one log in it, but first we'll have to use all those log properties to condense two or three logs into one. I also talk about the common mistake you don't want to make.
Change of Base Formula
The change of base formula is something every student is confused by, but it's not so bad: it basically allows you to find logs on your calculator using bases other than e and 10. Once you see a few examples, the confusion will end.
Log Properties
This video is all about those three formulas that turn log addition into multiplication, subtraction into division, and coefficients into exponents. The examples I work involve condensing logs (turning a few into one) and expanding logs (the opposite).
Evaluating Logs & Solving Basic Log Equations
In this video I cover the basics of logarithms, starting with what the heck they are and how to "evaluate" them. That basically means doing "simple" logs in your head by rearranging them into exponentials, which believe it or not you'll look back fondly upon once you see these crazy log things.
In this chapter you'll get all the basics on logarithms (logs) and log equations, as well as how to graph them and use them to solve tough exponential equations. I also devote a video to the difference between graphing logs vs graphing exponentials.
Word Problems: Exponential Growth & Decay
These problems use logs, so check out the logs chapter first if you're lost on those. The examples I work include exponential growth of a rabbit population, more compound interest, and radioactive decay including working with half-life.
Solving Exponential Equations Using Logs
Sometimes you can't match bases to solve exponentials, like in 3x = 5x-7, and you have to take the log of both sides! If you don't know logs yet, you'll need to jump ahead and watch the first few videos on logs in the next chapter before doubling back here.
Solving Exponential Equations (by matching bases)
In the logs chapter we'll get into harder problems. This video is about the easier half of exponential equations you'll have to solve: using exponent trickery to manipulate the two sides of the equation to have the same base, thus allowing us to assume the exponents are equal.
Graphing Exponentials
As with all functions, plugging in points is a great way to graph. Tip: When doing a transformation on an exponential function, do any flips and inversions before vertical and horizontal shifts, and don't forget that exponentials always always always have a horizontal asymptote (logs have vertical).
Compound Interest
Interest as in money, not interest. Compounded monthly. Compounded quarterly. Compounded semi-annually on a quarterly basis daily. The terms get confusing, but I'll get you through A=Pert and A=P(1+e/n)nt and the terminology that goes with it. And hey, you get to use your calculator!