D.E.V. PROJECT 2014ROCIO ALMARALES

INVERSES!

Step #1: Switch f(x) in the equation to x=, also switch all x’s in the equation to y’s.

Step #2: Multiply the denominator (y-2) to both sides. This way the y-2 on the original side cancels out the other.

INVERSES CONTINUED…Step #3: Next, Distribute the

x into the (y-2) on the left side to get….. xy-2x=4y-9

Step #4: Next we must get all the y’s on one side and x’s on the other side. In order to do this we must subtract xy from both sides of the equation. Then add 9 to both sides of the equation.

INVERSES CONTINUED…Step #5: Next we must

factor out the y from 4y-xy in order to get the y by itself, considering that this is what we are trying to solve for.

Step #6: Divide both sides of the equation by 4-x to get the y by itself.

Step #7: Change the y at the end of the equation to f-1(x) to identify that it is the inverse of the function we began with.

FARMER TED TAKEOVER!

Farmer Ted has 16,200ft. of fencing. He wants to fence off a rectangular field for his magical unicorns who desperately need a home. Please help Farmer Ted find the maximum area of his fenced off field! He’s running out of time!

FARMER TED!Step #1: We must help Farmer Ted get his fence built quick! But how do we begin? Well first we must be aware of the equations that take place when finding the maximum area. The two equations we use when searching for this maximum area is the area equation (A=xy) and the perimeter equation (2x=2y)

FARMER TED!Step #2:Next, we must

insert the perimeter, which is 16,200ft., into the perimeter equation.

Step #3:We must try and get y by itself because we are going to need it later in this process! We are going to do this by dividing both sides y 2!

Step #4: After dividing both sides by 2, subtract x from both sides to finally get y by itself!

FARMER TED! Step #5: Now going back to the

perimeter equation, we are going to insert what we solved for y in the perimeter equation into the area equation.

Step#6: Next we distribute the x so we can get an A and a B value.

Step #7: Since we now do have an A and a B value we can use the equation –b/2a to find our x-value.

Step #8: Insert your A value, 8,100, and your B value, -1, solve, and you will end up with 4,050.

FARMER TED!Step #9: Insert this value

into the equation we began with when we first inserted 8,100 into the area equation.

Step #10: Calculate your answer and you will see that we end up with 16,402,500 square feet. Which is our maximum area!

SIMPLIFYING RATIONAL EXPRESSIONS Step #1: When adding or

subtracting fractions, we must identify that in order to do so, we must have common denominators.

Step #2: To achieve common denominators we must multiply each of the denominators to both sides. Also, we must realize that if we multiply something to the denominators, we must also multiply those values to the numerator to balance out the equation.

Step #4: When you look at the denominators of both of the Fractions, you can realize that they are the same, both (6b-4)(b+6). In the process of adding and subtracting fractions, when the denominators are the same you just leave them as they are (as (6b-4)(b+6)

SIMPLIFYING RATIONAL EXPRESSIONS Step #5: Next you will need to

combine like terms in the numerator if possible. If it was not possible then you would just leave it as is, but in this case it is possible.

Step #6: After combining like terms you will end up with the most simplified form of this expression.

COMPLETING THE SQUARE Step #1: Always in a completing

the square equation one must start off by subtracting the beginning c-value, which in this case is 18.

Step #2: Now you are left with an equation… but no C value? We must use (b/2) squared to find the perfect C value! After you plug in your B value, -6, into the equation you see that 9 is your perfect C-value!

COMPLETING THE SQUARE Step #3: Since it is the perfect c-value you

must also add it to the other side to keep the equation balanced.

Step#4: There are too ways to go about this next step. One way you could get the value (x-3) squared is to factor them. Factoring is just finding the two sets of factors that if distributed would give you the quadratic we began with. Since the factors of this equation are the same, they are both (x-3) you can write them as (x-3) squared. But there is also a shortcut, in all of these types of equations there is a pattern, you can just divide the B-value in the quadratic. As you can see that would also give you -3!

Step #5: After this long process, all that is left to do is add nine to both sides to get everything back on one side! And now your done!