Professor Sherlock Mcmerlock Are Traveling to the Lost Island of Laplaya. (Math)

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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 f(x) has two real rational solutions and and g(x) has two real irrational 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. When the function crosses the x axis meaning f(x) = 0 there are two real numbers of x that satisfy the equation. Numbers where you can't write them as a fraction, and thus can't write them as a decimal which repeats are irrational. 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. Factor the a value out of the first two

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