During this project, I learned about the 3 different equations and converting each of them into each other, I also learned how to  size the lines according to the ones on my initials, you can see the expression I used for domain inside the swirly brackets {} at the end of each of the equations. There was nothing I really found extremely hard during the making of the assignment, but some things I found were annoying in the making of this assignment was converting the equations so that it matched the criteria of all 3 equations displayed at least once per letter. I found this hard because there were sometimes I would make a carless mistake and it would effect the rest of my conversion.

This week, I learned about Slope y intercept, an example is…

first, we got the pair of numbers, then we put it into a T-chart with the left numbers being the input and the right numbers being the output, on the T-chart we see the output numbers are going up by 5 so that’ll be the slope number with x and when we multiply 5 by the input numbers, we still need to subtract it by 2 to equal its output partner, so, -2 would be our y intercept. When we put it into our slope y intercept formula which is y=mx+b which we then get y=5x-2.

This week I learned how to determine steepness of a line, Ex…

before we calculate for the slope, we need to know what the different slopes mean. First we got a positive slope which is on the very right, then we got a negative slope beside it, we then have a normal horizontal line which has a slope of zero always, lastly, we have a normal vertical line which is has an undefined slope.

then we have to know the formula to calculate slope. On this formula, “m” represents slope, and the y numbers as the numerator are the output numbers and the x numbers as the denominator are the input number, and example is…

in this example, we got our 2 coordinates to find the slope of and we first plug the x and y values into our formula, as you can see the yellow underlined numbers are our y values and the green underlined numbers are our x values. Then, we do the subtraction we end up with the slope (m) 1/2 or 2.

This week I learned what functions are. All functions are relations but some relations are not functions, Ex…

A function is a shape on a graph in which the input number (x) has only one partner as the output (y). As you can see, on the example on the right, the numbers on the left circle (input) have only one partner with the right circle (output). On the example on the left, you can see that one of the input numbers (b) is partners with 2 and 3, which doesn’t make it a function. An ex on a number line..

an example of a function on a graph is this example, as you can see no lines overlap each other on the x axis.

this example shows a relation on a graph, as you can see, there are multiple points that overlap each other on the x axis, making this a relation.

One thing I learned this week was set notation and interval notation, some examples are.

when you use set notation with the domain, you use the greater/less then signs to show what space the domain covers on the x axis, in this example, x is less then 4 on the line so you can see that the domain is going to the left and since it does not state where x stops so it goes left forever until it reaches -∞. For interval notations, you first have to put a “D=” which stands for “domain”, when you look at it, it looks like a coordinate on a graph, but the brackets are what tells you everything, when the brackets are rounded it means that it is an open dot which means its not counted when you would do the numbers, if its a closed dot which means it can be applied to the numbers, you use [ ] brackets. Ex.

as you can see in this example, there is an closed dot which means the equation used squared and rounded brackets to express if its an open or closed dot.

One thing I learned this week was relations, the way I solve relations is…

As you can see in the T-chart on the Y side, the numbers are going up by 12, so if we want to find the relation between the X and the Y, then we have to use the clues the t-chart gives us. Aas we have already stated, side Y is increasing by 12 so that gives us the first part of the equation which is 12x=y but if you were to do the math with one of the X values, lets use 1 for this example, 12×1=12 which wont work because the first number of Y is 14, for this we have to modify the equation so it equals 14, for this we add an “+2”. So now the equation becomes 12x+2+y which works because 12×1=12+2=14.

too check if you got the equation right, you can implement the other values of X into your equation to see if it equals the Y value across from it.

One thing I feel will be on the mid-term test will be finding angles on a right triangle. The way I find angles on a right triangle is…

The first step to finding the angle is to first distinguish what ratio we are going to use by narrowing it down by using “SOHCAHTOA” and we can see that the Adjacent side doesn’t have a unit on its side so we take off the ratios that use adjacent which removes Cosine and Tangent, leaving us with a Sine ratio. Then, we put it into an equation.

The second step is solving. once we have our equation, the first thing we need to do is isolate the variable which is that zero with a line through it also known as theta. So, in order to isolate the variable, we move the Sine to the other side of the equal sign which turns it negative, also called an “Inverse Sine”. once we put this on our calculator, we should get the answer 33.1 if we rounding to nearest tenths, but if we are rounding to nears whole number then we will be left with 33 and make sure you put a degree sign on you answer so we would have an answer of 33°.

One thing I learned this week was factoring polynomials, examples on how to do this is…

First, there are three steps that you need to look for when factoring.

The first is to look if the numbers have anything in common in which you can divide them by, second and third is to see if the polynomial has 2 or 3 terms. If a polynomial has 2 terms or called a binomial, the first thing you need to look for is the difference of squares, in order for it to be a difference of squares all the numbers need to be perfect squares and their needs to be a minus sign, if any of these do not apply then it is not factorable, EX…

for the 3 terms called a trinomial, you have to make sure it follows the pattern of having an “x squared” a “normal x” and a “number” if these are met then in order to factor it you have to find two numbers that multiply to the number of the trinomial but also add-up to the coefficient of “x”, EX…

As you can see we have the pattern followed, now all we need to use is product and sum to factor, for this we have to look at all the 2 numbers that multiply to make 32 while also adding up to 12, as you can see the 4 and 8 are circled because multiplied they make 32 and added they make 12.

I learned last week how to multiply two binomials using area models, this week I learned how to multiply a binomial with a trinomial using area models

As you can see it is the same concept as using area models for 2 binomials but instead of it being a square we make a triangle because it has one side that is 3 squares long for our trinomial and 2 squares for out binomial. Once we have our numbers on the side of it, we multiply the numbers on the outside of the box and we should come out with 6 numbers and then we can combine the like terms like it shows the underlined numbers, once we combine the numbers we have out answer.

One Thing I learned this week was how to multiply binomials using area models which is basically simplifying it using 4 boxes, for example.

as you see we use the 4 boxes, we first put the numbers on the side and we multiply the number that are outside the box and put the answer in the box in between them. on the top of the box I wrote which number are being multiplied.

after you have all your numbers in the boxes, make sure you combine all the like terms, for example I underlined 35x and 8x because they are like terms that can be added together, In the end you should end up with your answer, the answer I got for my question is 14² + 43x + 20.