# Functions

The first part of the solution is easy as its a simple plus , minus. But the next part where it uses some functions is hard. Can you please explain it in a different way.

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Commented:
At the beginning of the problem, you were shown what the yield would be for 1 or 2 additional trees.

For 1 additional tree: Yield = (300 -1(10))  (20 + 1)
For 2: Yield = (300 -2(10))  (20 + 2)

What's different between those two? Only the values of 1 or 2. So for an unknown number of trees, replace the 1 or 2 with an X to get your formula:

Yield = (300 -X(10))  (20 + X)

Then transpose that to get:

Yield = (300 -10X)  (20 + X)

Note that 250 was used merely to simplify the formula. The author skipped a step, which is causing your confusion.

They started with this:

-10X^2 + 100X + 6000

And then both added and subtracted 250, for a net change of zero:

-10X^2 + 100X - 250 + 6000 + 250

And then simplified that into:

-10(X^2 - 10X + 25) + 6000 + 250
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Commented:
If you are satisfied with the first panel of the solution, fine. It ends with
Yield = (300 -2(10) x (20 + 2)
What do the numbers mean? (explained in panel one).
Note the 2. What is it?
It is the number of additional trees. You want to find the unknown number of additional trees wanted so call it x.
Replace the 2 with x. You get the equation at the start of panel 2. That equation is solved in the additional panels.
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Author Commented:
I am not understanding that how it makes this function?

Then Yield =( 300 – 10x) (20 + x)=.......
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Author Commented:
ok I understand this part. How the graph made based on quadratic equation?
a= -10
b= 100
c= 6000
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Author Commented:
Also next part where it says:  Complete the square to find the vertex of the parabola. Why not just use the quadratic function? How would I know to add 250 on both sides if i have similar question but different numbers.
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Author Commented:
Yield = (300 -10X)  (20 + X)

can you please tell me how you get this equation
-10X^2 + 100X + 6000
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Author Commented:
I still need more practice. Thank You.
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