Parabolas

Today in class we talked about parabolas. Mr. Vischak showed us a picture of a parabola, a hyperbola, and an elipse on his computer. There were two lines on each of these graphs. One connecting from the vertex and one from the focus. We learned another way to write eccentricity. mAB/mAC, with A B and C being the vertex focus and directrix respectively. We also learned how to write parabolic equations. y=a(x-h)^2+k is the standard form.

Hyperbolas- 2/10

Today we discussed hyperbolas, which can be confusing (especially the slope of their asymptotes), but once you memorize their properties you will dominate them.

Ellipses

Today we checked the worksheet and reviewed ellipses.

Notes for 2/3

Today we talked about the dot product of two vectors. Basically, if you have two vectors and want to find the dot product of them, you have to take the first term of each and multiply them together and add that to the second terms multiplied together (the dot product of vector "a" and vector "b" would be a1*b1 + a2*b2). We also learned the equation to find the angle between two vectors, as shown in the notes. By applying what we learned today about dot products and what we learn previously about vectors' magnitudes, we could figure out the angle. We proceeded to do a practice problem with this concept. Something to note about dot products is that if the dot product of any two vectors =0, the vectors are orthogonal (perpendicular in more than two dimensions). Another important thing is the diagram in the upper right-hand corner of the notes.

Notes for 2-2

Today we talked more about vectors especially how to combine them. We worked through several types of practice problems which all required you to be able to combine vectors. For example, one type of problem gives you 2 vectors and ask for a third which, when combined with the other 2, gives you a vector with 0 magnitude. For those, you add the i and j components of your vectors and the final one will have the same value but with the opposite symbol(+/-). Another type of problem we solved asked for the vector that would result when multiple vectors are combined. For those you just add the i and j components and if you need the angle, it helps to draw it out and think of the i component as the x value and the j component as the y value. One thing to note is that these problems are very similar to physics problems that involve vectors of forces.

Notes on 2/1

In class that day we learned about how to find the magnitude of a vector and how to find different components of vectors with magnitudes larger than one. We did a few example problems and we ended with a physics type problem in which a ball is thrown and we use vectors to find its maximum height. We also learned how to use "i" and "j" instead of the standard component form.

Today in class we learned about vectors. We started off class by talking about numbers. We graphed the number 3 on a number line. We found out that you can graph 3 in two ways. The first way is the literal number 3 on a line, so we placed a closed circle on the number 3. The second way we learned was you can use 3 as a value, which is shown on the second number line. We drew closed circles on 2 and 5 and drew a line connecting the two points and drew an arrow showing the direction in which we went. This shows us the difference between a number and a value; one closed circle on the number 3 was the number and 2 closed circles on 2 and 5 was the value 3. We next learned about the Component Form of a vector which goes as follows:

x(with a hat) = (the numbers with the 'a' and 'b' are there for coordinates only)

First off, the "hat" over the x in the picture is there to show that we are dealing with a vector, but on tests vectors will be shown in bold face. Second, we learned that the angled brackets tell us that we are dealing with a vector quantity.

To use the Component Form of a vector, all you have to do is plug in the coordinates for 2 vectors and do the algebra to get your answer.