This week, the question that really helped me learn was, If f(x) = (x + 2)², what is the vertex, line of symmetry, minimum, domain, and range? At first, I thought the vertex was (2, 0) because I saw the +2 inside the brackets and assumed it meant the graph shifted right. But after overlooking, I realized I had the direction of the shift backwards, and that mistake was what made everything click for me.

What I Learned:

For a quadratic in vertex form, f(x) = a(x – p)² + q

-The vertex is (p, q)

-The axis (line) of symmetry is x = p

-If a is greater than 0, the parabola opens upward and has a minimum at the vertex

-If a is less then 0, it opens downward and has a maximum value

In my equation, This means:

-Vertex: (–2, 0)

-Line of symmetry: x = –2

-Minimum value: 0 (at x = –2)

-Domain: All real numbers

-Range: y ≥ 0

This week, I learned about which method I should use to solve systems, an example is…

before we decide which method to use, we have to determine what situations we would use each of the methods, now, there is actually a third method where we can graph it, but its the hardest and most ineffective way in my opinion and these two are the best and most effective to use. an example with systems is…

On our first example, we can see that their is no isolated variable and once we see that, we automatically look towards elimination, which checks all the boxes which means elimination would be the best strategy.

In this example, we can see that their is an isolated variable so right off that we can see that substitution would be the best method, and although Elimination could be used for every system, it would be much easier to use substitution when there is an isolated variable.

One thing I learned this week was scientific notation, scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

when you have a big number with a lot of zeros, you move the decimal places until you reach the big number and put the important number as a decimal and when it is all zeros, you do the decimal number times 10 and however many decimal places you move it, that will be your exponent.