This week I worked on this initials project, which was:

1. Writing my initials on a graph
2. Finding points of each letter
3. Writing an equation for each line segment

It was a pretty straight forward project, I didn’t go through many challenges as I thought, and what worked for me was finding the slope quickly by using the slope formula:

This helped me a lot since each line segment had multiple plot points, so I could plug those in.

Here’s my final project:

Here are the equations of the first letter:

Second letter:

Third letter:

Last but not least, my first draft on paper:

photo

This week I learned how to find the slope of a line/equation.

For example:

Remember, when we want to find the slope, we need to isolate y. So lets move 5y to the other side, and switch the sign.

3x – 15 = 5y

Now divide everything by 5 so we can isolate the y.

m = ⅗

Done!

This week I learned how to find the slope of an equation, using y = mx + B. When I’m given a T chart, such as:

So if this is our T chart, the first step is to find how much they’re both going up by. Like x is going up by 2, but if we look at y, it also goes up by 2!

So, know we divide the difference between y and x to find the slope.

2/2 = 1!

This question has a slope of 1!

This week I learned about finding domain.

When we look for the domain, it means we’re looking for the numbers on the x axis. In this case its -4 and 0. But, we’re not done there, we have to include whether they are bigger, less than, or equal to x.

For example, x has to be bigger than -4, but since the dot on the number is not filled in, it means -4 is not included. It would look like this: -4 < x.

X has to be smaller than 0, and this time it does include 0 because the dot is filled in. That would look like: x ≤ 0.

To put it all together, the domain is -4 < x ≤ 0.

This week I learned that if a negative base inside a bracket is raised to an equal power, it turns positive. Here’s how:

=9

The exponent always applies to whatever is directly beside it, but in this case it’s a bracket. Whenever a bracket is raised to any power it means we are making copies of everything inside the bracket, including the negative. When we multiply two negatives together, we get a positive number. So that’s why when we raised it to the power of two, it turned positive because we made 2 copies of it. Same applies to any other even exponent, for example:

Since we already know it’s going to be positive, we can just go ahead and multiply the base together.

2  · 2 = 4

That’s our final answer.

This week I learned how to factor polynomials using the GCF method.

For example:

1. Find what both terms have in common. Which is 2, because 2 can divide into both. Also x, since both terms have x.

2. Factor it out by dividing everything by 2x.

3. add brackets, x goes goes first, then positive 3.

4. Add 2x on the outside since we factored it out

Done!

Another example:

1. Find GCF, which is 10, and a²

=10a²

2. Now we divide everything by 10a². Which is:

That is our answer!

This week I learned how to factor trinomials.

For example,

First, we find two factors of 15 that add to -2. BUT since its a negative 15, it means our answer must include a positive and a negative.

So two factors of 15 that add to -2 are -5 and 3. (-5 + 3 = -2)

Since there’s an x² we know that both brackets will include and x because x ⋅ x = x²

Now we add everything to the brackets, and our final answer will be:

(x -5)(x +3)

Another example,

This time its easier because everything is positive, which means our final answer will have no negatives.

First we find two factors of 16 that add to 10, which are 8 and 2. Again, since our first term is x² , we add an x to both brackets.

Now we put everything together and we should have:

(x +8)(x +3)

all examples by me 🙂

This week I learned to multiply binomials. For example:

First we multiply everything in the first bracket by each term in the second bracket using FOIL. (First, outer, inner, last)

Our answer should be 2a + 2c + ac + c²

Another example would be:

Again we simplify by using FOIL

And our answer should be 3x²+ cx +6x + 2c

All examples by me