Wonky Initials Project

Original Plan:

Completed Initials:

Equations for each letter:

This project helped me get better at writing equations. I think writing the rise over run was the easiest because I got lots of practice before I did on Desmos. For example, I practiced on paper and had to find the rise/run for different lines. The most challenging part was writing the whole equation in general. For example, if I wrote the wrong number, the whole line would change. It was also a little confusing at the start but once I wrote more equations, it got easier, and I was able to understand how to do it. 

What did I learn this week?

This week I learned how to solve Slopes.

For example, this is the equation: (1,5) and (5,13)….. First, you have to make a T chart and label the top “x,y”. (1,5) will be on top of (5,13). Then we count how much it takes for 1 to get to 5. Then we do the same with 5-13. Then we put it in a fraction. It should look like this: 8/4 because y goes over x. Then we divide the two numbers.. 8/4=2. To create the equation we use the slope 2x. Using the T chart we do 1×2=2 and see how much it takes to get from 2-5. We do the same with 5×2=10 and do 10-13. The answer is 3 numbers apart. Then we finish the equation. The final answer will be “y = 2x+3”.

I also learned Slope intercept form.

For example these are the numbers given: 5,8,11… First we see how many numbers apart they are from each other. The answer is 3 numbers apart. Then we do 3×1 3×2 and 3×3. The answer is 3,6,9. Then we put those number in order under 5,8,11. Then we see how much it takes for 3 to get to 5. Then 6-8 and 9-11. The amount is +2. Then to start off the equation we make the slope 3x. The final equation is “3x+2 = y”.

What did I learn this week?

This week, I learned the introduction to SLOPE. (rate of change)

Slope is a number that describes the steepness of a line…. It is the same as the tangent ratio.

For example, when finding the SLOPE, you do Rise/Run. That also means y/x and it is the Tangent. When doing the Slope equation, you use “m =”.

I also learned how to know if a line on a graph is negative or positive.

For example, if this is the line: ⟋ it is a positive and when the line is ⟍ it is a negative. ⎯ will equal 0 and | will be undefined.

What did I learn this week?

This week I learned function notation.

For example: Mapping notation

f is the name, x is the input, and 2x + 3 is the output. If “f : 5 –> 13“, on a graph it would look like this: (5,13), 5 is the input and 13 is the output. That way, it is easy to graph. It would be the same if it looked like this: g : r –> πr². g would still be the name of the function. r would still be the input, and πr² would be the output.

When doing function notation, It will look like this f(x) = 2x + 3. When it says f(x) it does not mean “f multiplied by x” it means “f of x”.

I also learned how to solve Function Notation. For example, this is the equation:

Function g is defined by g(x) = 6 – x².

Evaluate a:  g(4)

To solve this equation we have to put 4 where x is. “g(x)” does not mean g multiplied by x, it means g of x. So, we replace all x’s with 4. It will look like this, “g(4) = 6 – 4²” . Then we multiply the exponent first. So, 4² = 16. Then we calculate the remaining steps. 6-16 = -10. The final answer is g(4) = -10

What did I learn this week?

This week I learned how to find the x and y-intercepts.

For example, we have to find the y-intercept of this equation: 2y + 3x – 12 = 0….. First we replace x with 0 and multiply 3 by 0. Then we are just left with 2y – 12 = 0. We move the -12 to the other side and it will turn into +12. The equation will now look like this: 2y = 0 + 12. After that, we have to simply, so it will look like this: 2y/2 = 12/2. Once it is divided the final answer will be y=6.

The next equation will be to find the x-intercept.

For example, this is the equation: y = 2x – 8… First we make it y(0) and then the equation will simply look like this.. 2x = 8. Then we simply both of the numbers by 2 because we use the number beside the x. Then it will be 2x/2 = 8/2. The final answer is x=4.

What did I learn this week?

This week we reviewed Linear Relations. I learned about the Independent and Dependent Variable.

For example, the Independent variable is the Input, the “x” and the Domain. The Domain is the set of all possible inputs for the function.

Then the Dependent variable. For example, it is the output, the “y” and the range. The range is the set of its possible output values.

This is the equation:  (x = 1,2,3) and (y = 6.20, 12.40, 18.60)…. The input in the equation is x,1,2,3 and the output is y, 6.20, 12.40, 18.60.

What did I learn this week?

This week I was reviewing all the units. I learned something new when completely factoring polynomials.

For example, this is the equation: 9x² + 25… For this equation, it is impossible to factor. So, you just write “cannot factor”. You can’t factor this equation because it’s basically like writing 9x² + 0x + 25 and you would not be able to get to the middle number. To get to +25 it would be +5 multiplied by +5 and if we add those two numbers, it would equal 10 and not 0. Which means we would need one negative number to equal 0.

Another thing I learned was to solve polynomials in fractions.

For example this is the equation: (3x² y) (4x^³ y) ^–²…. For this equation, there is a negative exponent so we will have to turn the equation into a fraction. Then, we make two copies because of the exponent. It will look like this: 3x² y / 4x^³ y • 4x^³ y. Then we multiply the like terms. The final equation will look like this: 3x² y / 16x^⁶ y²..

What did I learn this week?

This week I learned patterns in polynomials.

I learned how to solve polynomials with exponents. For example, if the equation was ( x + 5)²   instead of distributing the exponent, we will make copies of the equation. Then It will look like this.. (x + 5 ) ( x + 5 ). The reason we make copies instead of distributing is because both the answers will be different.

Another example is when the equation looks like this.. 2 ( x + 4)² . We would do the same thing except we would not make copies of the 2. For example we would make copies of the equation except the 2. Then the equation would look like this.. 2 ( x + 4 ) ( x + 4 ). To solve that we would use the distribution law between the two equations in the brackets. Then after that is solved, we will distribute the 2 into the brackets. The final answer will look like this.. 2x²  + 16x + 32.

What did I learn this week?

This week we reviewed Polynomials. I also learned how to multiply polynomials using different methods. There are different types of polynomials. For example:

Monomial: 3x  ( One term)

Binomial: 3x + 5x  (Two terms)

Trinomial: 5x – 3x²  + 20  (Three terms)

One method is algebra tiles. For example, to solve 2x ( x + 1 ) we would make two horizontal rectangles side by side. Those represent the “2x” in the equation. Then one vertical rectangle on the left side of the two horizontal rectangles. That represents the “x” in the equation. Then at the bottom of the vertical rectangle, we will make one small square that represents the (+ 1 ).

The next method I learned was the distributive law. For example, if the equation was 2 ( 3x – 10 ) we would multiply the 2 with the 3x then the 2 with the -10. Then that would equal 6x – 20. Since there are no like terms we cannot simplify, so that would be the final answer.

Photo Citation:

Factoring Resources