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Algebra 2 Portfolio - Second Quarter

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Airiel Vega

on 7 January 2013

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Transcript of Algebra 2 Portfolio - Second Quarter

Algebra 2 Second Quarter Portfolio Linear Equations Identifying Functions Point-Slope Form y-y = m(x-x ) (-10,3) (-2,-5) Example: -5-3 -2+10 =-1=m y-3=-1(x+10) To solve this problem you have to first find the slope. You do y-y over x-x . Then you put the one of the pairs of coordinates into the formula. You fill in y and x with one of the pairs of coordinates. When we first did this formula, I couldn't remember how to do it or fill in the right coordinates for the variables. Once I remembered which variables I filled in with coordinates, I knew how to do the formula. I just had to find the slope and then that's it. Slope Intercept Form y=mx+b Example: Slope of 3 that goes through (1,5) 5=3(1)+b 5=3+b -3 -3 2=b y=3x+2 To solve this problem you have to fill the x and y variables into the formula to find b. Once you find b, you fill in the slope and b into the formula to get your equation. At first I didn't know what b was or how to find it. Once I knew that I had to put in the coordinates in place of the variables and simplify it down to b, I could find b. I also didn't know which variables I had to substitute when finishing the equation but now I know you put in the slope and b. Standard Form Ax+By=C Example: y= 1 2 x-2 + 1 2 + 1 2 1 2 x x x + y ( ) = -2 ( ) 2 2 -x + 2y = -4 To solve a standard form problem, first you get x and y on the same side of the equal sign. You have to put x first and then y after. If you have any decimals or fractions, you want to make the numbers integers so you multiply each side by a number, in this case its 2, and then you have your answer. At first I didn't know how to do this formula because I didn't know what A B and C stood for. Then I thought I was done with the problem but I didn't have integers for my coefficients so I would have to make them integers. It got me really confused but once I started doing those problems I got the hang of it. Parallel Lines They have the same slope Example: y=3x+2 Line Parallel to: y=3x-1 To solve this kind of problem, all you have to do is put the same formula in but change the b. You use the same slope and you have the x and y and then you just change where on the y-axis the line is but it will be parallel to the original line as long as it has the same slope. When we first did this kind of problem I didn't get how it would be parallel if it has the same slope and how to pick what point to use for b. When I finally tried it on a graph I figured out how it made sense. I didn't think that changing the slope would make the line tilt another way. Then I finally realized that you could practically pick any point to use as your b as long as you kept the same slope. Airiel Vega Example: (-2,-1) (-1,0) (6,3) (-2,1) Domain: Range: -2 -1 6 -1 0 1 3 Not a function Domain: Range: (11, -2) (12,-1) (13,-2) (20,7) 11 12 13 20 -2 -1 7 Is a function To identify whether a set of ordered pairs are a function you have to split them up into domain and range. The domains are the X's and the ranges are the Y's. You can draw arrows to each set of pairs. If there is a number in the domain that matches with two numbers from the range then it is not a function. It has to have only one range value for each domain. If there are two numbers in the domain that match with one range, it is still a function. At first I didn't know how to figure out if a set of ordered pairs is a function. I couldn't remember whether it was the domain or range that couldn't have two number values for it to not be a function. Once I remembered that the domain can't have the same number going to two different ranges, I knew how to tell whether it was a function or not. Vertical Line Test Example: Function Not a function If you draw vertical lines through each point and the line only goes through one point, it is a function. If the line goes through two points it isn't a function. I didn't know what the vertical line test meant and when I drew the graphs I still didn't really get it. I would draw the lines connecting the points but I didn't get what lines you had to draw. Once I realized that if any of the lines went through more than one point it wasn't a function then I got it. Scatter Plot ~A graph that relates two sets of data by plotting the data as ordered pairs. Correlation~The strength of the relationship between the points. Line of best fit~The trend line that gives the most accurate model of related data. Correlation Coefficient~It indicates the strength of the correlation. Strong correlation Strong negative For a scatter plot, you plot the points that are in your coordinate pairs on the graph. Then you figure out the correlation, line of best fit, and correlation coefficient of the plotted points. I was fine with plotting the points on the graph but I had trouble at being able to read the correlation. Sometimes I couldn't tell if it was strong or weak because the lines were in between strong and weak. Then when I would try to do the line of best fit I wouldn't know where to put it. I also couldn't remember what each correlation coefficients looked like to match it with the scatter plots. Now I know how to read them by memorizing what each correlation looks like. Transformations Example 1: g(x) = f(x)+6 Vertical translation up 6 units Example 2: h(x) = 2f(x) Vertical compression 2 units To figure out what transformation the function is you have to know the formulas that tell you what each one is. The first example has the formula y=f(x)+K which means its a vertical translation however many units K is. The second example has the formula y=af(x) which means its a vertical compressions however many units a is. When we first learned this, I couldn't remember which formula went with which transformation so I kept putting the wrong transformations for the functions. Once I memorized which transformation went with which formula I was able to label the functions correctly. Real-Life Example: A phone company charges $22 payment and an extra $4 for every time you use the phone. So this linear function would be y = 4x + 22, where x is the number of times you use the phone and y is the total amount of money charged. Linear Function: The function is just a straight line that goes through the second and third quadrants on a graph.
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