Completing the Square: So many steps, such little time. It sounds like it involves a square or maybe this is a geometry problem? Why am I doing this again? Why must we complete the square in the first place?
These are all the thoughts that cross our minds when first learning how to complete the square. Well, I’m here to tell you there is a reason for all those steps and they aren’t that bad if you really break them down, let’s take a look!
I’m not going to lie to you here, there are a lot of seemingly meaningless steps to completing the square. The truth is though (as shocking as it may be), is that they are not meaningless, they do form a pattern, and that there is a reason! Before we dive into why let’s look at how to solve this step by step:
Feeling accomplished yet!? Confused? All normal feelings. There are many steps to this process so go back and review, practice, and pay close attention to where things get fuzzy.
But the big question is why are we doing these steps in the first place? Why does this work out, to begin with?
For those of you who are curious, continue to read below!
Want more Mathsux? Don’t forget to check out our Youtube channel and more below! And if you have any questions, please don’t hesitate to comment below. Happy Calculating!
Need more of an explanation? Check out why we complete the square in the first place here !
Howdy math friends! In this post, we are going to learn about solving trigonometric equations algebraically. This will combine our knowledge of algebra and trigonometry into one beautiful question! For more on trigonometric functions and right triangle trigonometry check out this post here.
Solving trigonometric equations. Sound complicated? Well, you are correct, that does sound complicated. Is it complicated? Hopefully, you won’t fund it that way after you’ve seen this example. We are going to do this step by step in the following regents question:
How do I answer this question?
The questions want us to solve for x.
Step 1: Pretend this was any other equation and you wanted to solve for x. Thinking that way, we can move radical 2 to the other side.
Step 3: Now we need a value for x. This is where I turn to my handy dandy reference triangle. (This is a complete reference tool that you should memorize know). For more on special triangles, check out this post here.
Step 5: Notice that cosine is positive in Quadrants I and IV. That means there are two values that x can be (one in each quadrant). We already have x=45º from Quadrant I. In order to get that other value in Quadrant IV, we must subtract 360º-45º=315º giving us our other value.
Does this make sense? Great! 🙂 Is it clear as mud? I have failed. But I have not given up (and neither should you). Ask more questions, look for the spots where you got lost, do more research and never give up! 🙂
Hopefully you enjoyed my short motivational speech. For more encouraging words and math, check out MathSux on the following websites! Sign up for FREE math videos, lessons, practice questions, and more. Thanks for stopping by and happy calculating! 🙂
Greetings math friends, students, and teachers I come in peace to review this piecewise functions NYS Regents question. Are they pieces of functions? Yes. Are they wise? Ah, yeah sure, why not? Let’s check out this piecewise functions NYS Regents question below and happy calculating! 🙂
1 value satisfies the equation because there is only one point on the graph where f(x) and g(x) meet.
Does the above madness make sense to you? Great!
Need more of an explanation? Keep going! There is a way to understand the above mess.
How do I read this?
Looking at this piece-wise function: We want to graph the function 2x+1 but only when the x-values are less than or equal to negative 1.
We also want to graph 2-x^2 but only when x is greater than the negative one.
One way to organize graphing each piece of a piecewise function is by making a chart.
Lets start by making a chart for the first part of our function 2x+1:
Is it all coming back to you now? Need more practice on piece-wise functions?Check out this link here and happy calculating! 🙂
Also, if you’re looking to nourish your mind or you know, procrastinate a bit check out and follow MathSux on these websites!
Hey math friends! In this post, we are going to go over Factor by Grouping, one of the many methods for factoring a quadratic equation. There are so many methods to factor quadratic equations, but this is a great choice, for when a is greater than 1. Also, if you need to review different types of factoring methods, just check out this link here. Stay curious and happy calculating! 🙂
Before we go any further, let’s just take a quick look at what a quadratic equation is:
Usually, we can just find the products, the sum, re-write the equation, solve for x, and be on our merry way. But if you notice, there is something special about the question below. The coefficient “a” is greater than 1/. This is where factor by grouping comes in handy!
Now that we know why and when we need to factor by grouping lets take a look at our Example:
Factor By Grouping: Hard to solve? No. Hard to remember? It can be, just remember to practice, practice practice! Also, if you are in need of a review of other methods of factoring quadratic equations, click this link here.
Want more Mathsux? Don’t forget to check out our Youtube channel and more below! And if you have any questions, please don’t hesitate to comment. Happy Calculating! 🙂
Ahoy math friends and welcome to Math Sux! In this post, we are going to learn about the equation of a circle, mainly how to write it when given a circle on a coordinate plane. We’ll see how to find the radius and center from the graphed circle and then see how to transfer that into our equation of a circle. And we’re going to do all of this step by step with the following Regents question. Stay curious and happy calculating! 🙂
How do I Answer this Question?
Let’s mark up this coordinate plane and take as much information away from it as possible. When looking at this coordinate plane, we can find the value of the circle’s center and the circle’s radius.
Now that found the center and radius, we can fit each into our equation:
The only equation that matches our center and radius, is choice (2).
If the above answer makes sense to you, that’s great! If you need a little further explanation, keep going!
Equation of a Circle:
Equation of a Circle: Let’s take a look at our answer and break down what each part means:
So what do you think of circles now? Not to shabby, ehh? 🙂
Looking for more on circles? Check out this post on how to find the Area of a Sector here!
Howdy math peeps! In this post, we are going to go over the recursive formula step by step by reviewing a Regent’s question. Yes, it is the recursive formula jam, well at least it’s my kind of jam. These things may look weird, confusing, and like a “what am I doing?” moment, but trust me they are no so bad!
How do I answer this question?
At first glance, all of these answer choices may look exactly the same. The first thing I would want to do with this question is to identify how all of theses answer choices are different. Take a look below:
What is the Recursive Formula?
A Recursive Formula is a formula that forms a sequence based on the previous term value. All this means is that it uses a formula to form a sequence-based pattern.
Let’s go through each choice to identify the answer:
Our goal is to test out each choice given, until we get the desired sequence: