SP#6: Unit J Concept 10 - Writing a repeating decimal as a rational number using geometric series

In order to fully understand this problem, we must pay attention to the repeating numbers. For example, in this problem, out repeating numbers are 24. We must remember to ignore to 10 (number in front of the decimal) and remember to add it in the end. We must always remember that we can only add fractions together if they have the same denominator. Other than that, the problem should be pretty clear. :) Thanks for viewing. :)

SP# 3: Unit I Concept 1: Graphing exponential functions and identifying x-intercept, y-intercept, asymptotes, domain, and range

The viewer needs to pay attention to certain points in order to fully understand this concept. For one, there can not be a x intercept if there is a negative because how can we take the natural log of a negative? Also, we must remember from previous chapters that x=0, and y=0, and we can find the x and y intercepts. Also, the domain will usually be all real numbers, meaning -infinity to +infinity. Lastly, we should remember that when looking for the asymptote, y=k. THANK YOU.

SP#2: Unit E Concept 7 - Graphing a polynomial and identifying all key parts

This problem is about graphing polynomails, including the x and y intercept (with multiplicities), end behavior. 

To begin with, I factored out the equation above which lead me to my zeros. My original equation was to the 4th power which means I need 4 zeros. When i factored out the equation, I ended up with 4 zeros. Also, since the original equation started with "x^4" (both positive = even positive) the graph will be going up whether it's going to infnity or negative infinity. We find the y-intercept by setting "x" to 0 in the original equation. After all that, we plot all the points given, and make sure the graph is going upwards both ways. :)

SP#1: Unit E Concept 1 - Graphing a quadratic and identifying all key parts

This problem is about identifying x-intercepts, y intercepts, the vertex, the axis of quadratics and how to graph it. Here's an example where I used my own example. 

To begin with, my problem was f(x)=2x^2+4x-16. I subtracted 16 on both sides which gave me 2x^2+4x=16. I then took out the coeficiant which is 2 and added it to the other side as well, and it gave me 2(x^2+2x)=16+2. After, I divided "b" by 2 which is 1 and squared it which is 1 and added 1 to both sides. I ended up with 2(x^2+2x+1)= 16+2(1). KEEP IN MIND THAT "2(x^2+2x+1)" FACTORS OUT. 2(x+1)^2=18. Subtract 18 over and we have the parent function equation which is 2(x+1)^2-18. The vertex is a minimum and is (-1,-18). To find the y intercept, we would need to set "x"=to 0 in the original equation which makes it (0,-16). The axis is "x=-1" because of the vertex. Now to find the x intercepts, we just need to solve, "2(x+1)^2=18" :)