D.E.V.

STONE DEVELOPS HIS
EXPERT VOICE
WITH HELP FROM OLIVIA AND ERICA

PROBLEM #1
Stone owns a potato farm in East Lansing next to the Red Cedar River. He
wanted to know how many potatoes he could farm with only 1687 feet of
fencing. One square foot produces exactly one ripe potato. Assuming the land
is along the Red Cedar, how many potatoes could he produce with the given
fencing?

PROBLEM #2
Stone is in math class and is reviewing how to complete the square. If he doesn’t get
the hang of this, he will never get into college to learn about the different kinds of
potatoes for his farm! Olivia and Erica come to the rescue! They come up with a
practice equation to help explain.
Here it is:
1062=36x²+16x-154

PROBLEM #3
On Stone’s potato farm, he is celebrating the one year anniversary of his business. To
kick of the party, he decides to set off some fireworks. A firework is launched off of a
3.5 meter high platform. It travels at a speed of 10.9 meters per second. This is
displayed in the equation y=-4.9x2+10.9x+3.5, where y=height and x=time. Find the
inverse equation to figure out the time at which the remains of the firework hit the
ground so Stone knows when to set off the next round of explosions.

PROBLEM #4
Stone is a fan of fractions. He loves to find domains! However, this time he is given the
domain and has to figure out the corresponding equation. Once again, Olivia and Erica come
to the rescue!
The problem is as follows: Find the equation for the domain D: (- ∞,-5] u [7,8) u (8, ∞)

.

By the brackets being square or curved we know if the
number is included in the domain. Square brackets
mean they are included, curved mean they are not.

•

We know that the 8 must be in the denominator
because x cannot equal zero. You cannot divide by
zero, so to make the denominator equal zero, the
value is x-8.

This leaves the -5 and 7. To make these values equal
0, you use the opposite of these numbers ((x+5)(x-7)).
Then, distribute these. You know they need to go
under a radical because they are included in the
domain and under a radical you can have a value of 0.

Step 1: Factor to more easily identify holes and the x-intercepts.
Do so by taking out the greatest common factor and figuring the
factors of the third term that add up to equal the second term.
•

Step 2: Determine if there is a hole. When there is a factor that
is the same in both the numerator and the denominator the
hole is at the x-value that make the factor equal zero.

Step 3: In order to find the x-intercepts you have to discover
where the numerator equals zero. Set each factor to zero and
solve.
Step 4: To determine the y-intercepts you set x equal to 0. Use
the original equation to solve.
Step 5: Vertical asymptotes occur when the denominator equal
zero. To find vertical asymptotes you have to set the
denominator equal to zero and solve.
Step 6: To find horizontal asymptotes it depends on the highest
power of the numerator and denominator. If they are the same
in both then it is just the fraction of the leading coefficients.
Look at the original equation.

PROBLEM #6
In Stone’s college acceptance test, he is pushed to the limit. A lot is at stake because he
wants to explore the art of potato growing further at his future college. The final
question is to graph the equation x⁴+9xᶾ
-33x²-244x+672. Using previous knowledge
from tutor sessions with Olivia and Erica, Stone goes to work. He realizes he needs to
long divide, and is told that the quadratic x²+4x-32 can divide into the fourth power
polynomial. His work is as follows…

Step 1: Divide the first term in the dividend by the first term outside
of the division bracket. Write this above the first term in the
dividend.
x²+5x-21
x²+4x-32

x⁴+9xᶾ
-33x²-244x+672
-(x⁴+4xᶾ
-32x²)

Step 2: Multiply the first term outside the division bracket by the
quotient you put on top of the division bracket. Write the product
below the first term of the dividend.
Step 3: Repeat Step 2 with the second and third terms outside of the
division bracket, writing the products below the corresponding terms
of the dividend.

5xᶾ-1x² -244x
-(5xᶾ
-20x²-160x)
-21x² -84x+672
-(-21x² -84x+672)
0
(x²+4x-32) (x²+5x-21)

Step 4: Subtract that row of terms from the term above.
Step 5: Divide the first term of difference by the first term outside of
the division bracket. Write this above the corresponding term on top
of the division bracket.

(x+8) (x-4) (x-3) (x+7)
x=-8 x=4

x=3 x=-7

Step 6: Repeat Steps 2- 5 until you get a difference of 0.
Step 7: Take the two quadratics and factor as in problem 5, step 1.
Step 8: Solve for x.

x=-8 x=4

x=3 x=-7

The x values we found are the x- intercepts. So,
we know that the graph goes through -8, -7, 3,
and 4.
Because the first term is to the fourth power, it
is an even graph, meaning that both ends aim
towards the same direction.
The first term is positive and therefore as x
approaches infinity, y approaches infinity as
well. As x approaches negative infinity, y
approaches infinity.

THANKS TO THE HELP FROM OLIVIA AND ERICA,
STONE ACES THE TEST AND LEAVES DREAMING
OF HIS FUTURE SUCCESS!

D.E.V.

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