Question

Are you ready for adventure? You bet you are!

For this adventure, you and world renowned Professor Sherlock McMerlock are traveling to the Lost Island of Laplaya. When the boat arrives on the island shore, you and Professor McMerlock disembark on your adventure. You trudge through the jungles and arrive at three impressively large doors. About eye level on each door is an intricately carved keyhole. Directions are scratched into the wood above each keyhole.

Answer 1

To open these doors, you must match the number and type of solutions for the following two fuctions in standard form.
f(x) = x2 + 6x – 16
g(x) = x2 +6x + 1
Match the following descriptions of the solutions to each of the functions above.
Hint: they each have their own match.

Two real irrationals solutions
Two real rationals solutions
After matching these functions, explain to Professor McMerlock how you know these functions meet each condition. Remember, he is a professor, so use complete sentences.

Like magic, the doors creak open with a burst of dust, musty air, and shrieking bats. You lead McMerlock down the first corridor. It is so dark that you can barely see your own outstretched hand. The darkness consumes you as you continue to trek deeper and deeper in the hallway. Suddenly, a mystical suit of armor blocks your path. A voice emanates from inside it.

“To pass by me, you must tell me how to convert standard form into the general, vertex form... I have a test on it next week.”
Explain how to convert f(x) into the general, vertex form of the equation. Use complete sentences.

Satisfied with his notes, the guardian lets you pass into the next chamber. As you enter the dimly lit room, McMerlock points out that the floor tiles have numbers on them, and that some floor tiles are missing. On the ceiling is painted a cryptic message.

“Only the solutions of g(x) will lead you safely across.”
Find the solutions of g(x). Show each step.

You can feel the treasure of the Lost Island of Laplaya in your grasp, as you deftly step on the correctly numbered stones. A wise old woman sits in front of the treasure. You can hear the crackle of magic coursing through her fingertips. The wise old woman grants you the treasure of the Lost Island of Laplaya! The treasure is an awesome ability to complete the square! Way to go! Professor McMerlock is thankful he picked you and promises to call on you again for another adventure.

Answer 2

omg, haha, I did this assignment for my flvs algebra 2 course XD

Answer 3

I don't think you want my help though... I got a terrible grade on it :\

Answer 4

Do you still have it on your computer?

Answer 5

I.... don't really know... I'll look for it...

Answer 6

yes, I have it...

Answer 7

that is a lot of words for a stupid math problem, isn't it?

Answer 8

secondly the words don't even make sense
\[f(x) = x^2 + 6x – 16\] is a function
i guess "solution" means to solve
\[x^2+6x-16=0\]

Answer 9

since this one factors as
\[(x-2)(x+8)=0\] the solutions are \(2\) and\(-8\) which are rational

Answer 10

the other one will have irrational solutions since they told you there are one of each
also if you solve using the quadratic formula, you will see that the solutions are irrationals

Answer 11

Explain how to convert \(f(x)\) into the general, vertex form of the equation. Use complete sentences.

There is no such thing as "general vertex form" there is however, vertex form
that looks like
\[f(x)=a(x-h)^2+k\]
in this case \(a=1\)
to find \(h\) the first coordinate of the vertex is always \(-\frac{b}{2a}\) which in this case is \(-\frac{6}{2}=-3\)
the second coordinate of the vertex is \(f(-3)=(-3)^2+6\times (-3)+16=9-18-16=-25\)
making the vertex form
\[f(x)=(x+3)^2-25\]

Answer 12

Find the solutions of g(x). Show each step.\[x^2+6x+1=0\\
x^2+6x=-1\\
(x+3)^2=-1+8\\
(x+3)^2=8\\
x+3=\pm\sqrt8\\
x=-3\pm\sqrt8\] or if you prefer
\[x=-3\pm2\sqrt2\]

Answer 13

I like the @satellite73 's first comment

Answer 14

@satellite73 Is that it?