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.
- To open these doors, you must match the number and type of solutions for the following two functions 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
2. “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.
3.“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.