SP#7: Unit Q Concept 2: Finding All Trig Function Values Using Identities

 

 

This SP was made in collaboration with Leslie E. Please visit the other awesome posts on their blog by going here

 

Identities

 

 

SOH CAH TOA

The viewer must need to understand what identities are and how to use them for this problem. The viewer needs to be aware of the substituting that goes on while trying to find all trig functions. The viewer must be familiar with SOH CAH TOA in order to do the problem the other way. They need to pay attention to the ratios when solving it with SOH CAH TOA.

SP#5: Unit J Concept 6: Partial Fraction Decomposition with Repeated Factors

The viewer must pay attention to the common factors. You need to pay attention to the factors and count them because that is how many times there will be an exponent. The viewer needs to distribute and combine properly because small mistakes can be made in this area. The viewer needs to look at how many systems there are in order to have the same amount of variables. 

SP#4: Unit J Concept 5: Partial Decomposition w. distinct factors

The first thing we do is compose. This means we multiply by the bottom numbers and then we get a larger fraction. (you first have have to combine like terms)

This part is decomposing. You have to find what multiplied into this large fraction to get there.

Type in what you end up with in the calculator. You should end up with what you started with.

This shows that once I checked it, it was right.

 

The viewer needs to pay attention to combining like terms in order to get the problem right. The viewer must pay attention on the least common denominator. The viewer needs to make sure their answer is correct after checking it with what the problem originally was. This can be checked in the calculator. 

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

The viewer needs to pay special attention to the a. The a tells you if it is above or below. The viewer must also pay atention to the k because that is the asymptote. The viewer must pay attention to y=k, meaning that there are no x-value restrictions, so the domain is all real numbers. Also, the viewer must pay attention to the asymptote because the range depends on that. Another thing is that the viewer must pay attention and understand why there is no x-intercept.

SP #2: Unit E Concept 7: Graphing Polynomials, uncluding: x-int, y-int, zeroes (with multiplicities), end behavior.

This problem is about solving a polynomial with a fourth degree and then graphing it. To find the x-intercepts, you must factor the polynomial. From here, you can find the multiplicities of it. Once knowing what the multiplicities are, then you will know if it will go through, bounce, or curve.

The viewer needs to pay special attention to the leading coefficient. This is the key to finding out how the graph will look like. The viewer must also pay attention to the multiplicities. The multiplicities will say if it goes through, bounce, or curves.

SP #1: Unit E Concept 1: Identifying x-intercepts, y-intercepts, vertex (max/min), axis of quadratics and graphing them.

This problem is about sketching graphs of quadratics using shifts of the parent function accurately with the graphing calculator. The equation begins in standard form, which is f(x)= ax^2+bx+c. To make it simpler, we must complete the square to make it : f(x)=a(x-h)^2+k. The graph will have as much as 4 points which are: the 2 x-intercepts, the y-intercept, and the vertex.The axis will be a dotted line.

The viewer must pay close attention to see if the graph if positive or negative because that will determine if it is a minimum or a maximum. In this example, it is positive, and this makes it a minimum. The h and k values are what make the vertex of your graph. If the h is negative, then the x on the vertex will be positive (and vice-versa). The k stays what it is. Also, the axis is not just a number; it is x=__.