Graphing Polynomials

Another Fun round of Math!

I know math is not the fun class but I am really enjoying study the subject this year, within 2018 – 2019 I got to learn about Precalculus, which includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Ever thought, algebra and trigonometry is not my strength I still want to build those skill into my strength. This round we are studying in Chapter 3 (Polynomial and Rational Functions), which include seven smaller subjects. I would like to show some example in the small subjects that related to Chapter 3.    

In Chapter 3.2 (Polynomial Functions and Their Graphs) we learn the polynomial functions simply as polynomials. The following polynomial has degree 5 leading coefficient 3, and constant term -6

Polynomial Equation Layout

We also need to understand how the graph of a basic polynomial function look like and which graph is not a polynomial function.

Basic graph of polynomial function

Example: P(x)=x^4 − x^3 − 6x^2

First, we’ll need to factor this polynomial as much as possible so we can identify the zeros and get their multiplicities.

P(x )= x^4 − x^3 − 6x^2 = x^2(x^2 − x − 6) = x^2(x − 3)(x + 2)

Here is a list of the zeroes and their multiplicities.

X = −2 (multiplicity 1)

X = 0 (multiplicity 2)

X = 3 (multiplicity 1)

So, the zeros at x = -2 and x = 3 which will correspond to x-intercepts, that cross the x-axis since their multiplicity is odd. The zero at x = 0 will not cross the x-axis since it multicity is even. The y-intercept is (0,0) and notices that this is also an x-intercept.

The coefficient of the 4th-degree term is positive and so since the degree is even we know that the polynomial will have a positive infinite bound at both ends of the graph.

Finally, here are some function that helps to the graph, We need to plug in a random number to help identify the behavior of the graph. Normally, we would have one point in between the zeros.  

P(−3) = 54

P(−1) = −4

P(1) = −6

P(4) = 96

Here is a sketch of a graph

Sketch of a Graph x^4 – x^3 – 6x^2

SAT Preparation

On the first two weeks of the school year, we did PSAT Bootcamp. We had Amanda and Kim to be our mentors. For the two weeks we work with Kim and Amanda, they taught us many skill and strategy about SAT. I found the Reading and Language section was the hardest subject that blocking me from getting a high score when they took the test for the second English learner.

These are the resources that help us practics from SAT.

We took three PSAT over two weeks of practice with a website called Khan Academy, I can see really clear the improvement that I made when working with Kim and Amanda beside learning by myself. Also, I use the strategies that I learn with them to improve my score. After the first two weeks of the school year, in math class, we are still practicing for PSAT, by that we have independent time to work on some small subject like complex number and circle theorem. So that we can extend to a rage of math knowledge beside learning about the strategies.   






AP Statistics Course


  In math class, I am currently taking an AP statistics course. In this particular course, there are lots of efforts and times have to be put into it. I found it fun but also challenging at the same time since it’s a college level course with high vocabularies and plus English is my second language.


Desmos project

Atom had to run from the Talent Gym to boxing Arena. The distance between Talent Gym and Boxing Arena is 30 km. Atom start running for 1 hour then take a small break. After the break he took off again then stop for buying boxing gloves. Next he run out of the shop toward his destination. After the exhausted run he got in the flight and run back to the Gym

Which time interval did he run the fastest?
From time 3 hour 30 minutes to 4 hour 15 minutes 36 second
What is the speed?
17 km/h

At what time did he reach his destination?
In 4 hour 15 minutes 36 second

What is the average speed from starting point until he reach the arena?
average speed 7.04

What time did he arrive the Gym
In 8 hours 15 minutes 36 second