Archive | April, 2017


8 Apr

In this semester we’ve learned several topics such as linear functions, average rates of change and polynomial in the short-run and the long-run, exponential function, and quadratic functions. I don’t think pre-calculus has been much different than the math I learned in high school. Calculating the average rate of change was surprising to me because it was something new that I never learned. The most interesting idea was finding the roots. However the topic I had most trouble with was piecewise functions.

I think the idea Ill use the most is calculating the average rate of change. It is the change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value divided by the change in the x-value for two distinct points on the graph. Something I would like to go differently moving forward is having the professor teach more using the white board instead of desmos.

What do you want to do differently going forward?

Imagine All The Numbers

5 Apr

Complex does not mean complicated. A complex number is a combination of a real number and an imaginary number. Real numbers are basically any number you can think of and imaginary numbers when squared give you a negative result.

Screen shot 2017-04-04 at 12.46.32 AM

Ex) Add 3+5i and 4-3i

(3 + 5i) + (4 − 3i)
= 3 + 4 + (5 − 3)i
= 7 + 2i

An electromagnetic field, for example, requires imaginary numbers to measure because the strength of the field is determined by both electrical and magnetic components that must be combined into a single complex imaginary number to get an accurate measurement. Is my example helpful?


Fancy Factoring

3 Apr

x^3 – 5x +3x -15 – Factoring by group

In order to factor by grouping this polynomial we have to see if the terms have any GCF (Greatest Common Factor). In this case there is 1 GCF. Then we create smaller groups by grouping the first two terms together and the last two terms together which will be x^3 – 5x^2 + 3x – 15, then we factor out the GCF from each of the two groups and in this problem the signs in front of the 5x^2 and the 15 are different so you need to factor out a positive 3 which then you will get x^2(x – 5) + 3(x – 5), the thing that the groups have in common are the (x – 5) so you can factor that out which gives you (x – 5)(x^2+3), then see if any of the remaining factors can be factored which they cannot so that is the final answer

18x^2 – 98y^2  – Factoring the difference of squares

the two terms have 2 in common and gives us 2(9x^2 – 49^2), To factor this problem into the form (a + b)(a – b), you need to determine what squares will equal 9x2and what squared will equal 49y2. In this case the choices are 3x and 7y because (3x)(3x) = 9x2 and (7y)(7y) =49y^2 which gives us 2(3x + 7y)(3x – 7y)

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In the Long Run…

3 Apr

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The degree of the polynomial is the largest exponent on the variable. The leading coefficient in a polynomial is the highest degree term. The polynomial I created is x(1+3x^9), when zoomed out it looks like the function u(x) =5x^2 and when zoomed in it looks like the function q(x)=0.5x. Below the blue line represents u(x) =5x^2 and the red line is x(1+3x^9).

Screen Shot 2017-04-02 at 9.02.31 PM

Below the blue line is x(1+3x^9) and the red line is q(x)=0.5x.

Screen Shot 2017-04-02 at 9.21.29 PM

Any feedback on my polynomials?