PRE-CALCULUS UNIT EXAM 2

PRE-CALCULUS UNIT EXAM 2

Name:

109-11 Unit 2 Exam Again: all work must be shown to receive credit. 1. Use the quadratic equation to factor the function 𝑓(𝑥) = 𝑥2 + 6𝑥 − 11. Show that one of

the two results is correct by evaluating the function at that value.

1. State the equation of a function with a zero at 𝑥 = −2, a double zero at 𝑥 = 1, and a zero at 𝑥 = 4. Graph the function. (Hint: you may want to compress the vertical scale.)
2. Divide 3𝑥3 − 2𝑥2 − 31𝑥 + 30 by 𝑥 − 3 using the (written) technique of your choice.
3. Find all asymptotes of 2𝑥2−5𝑥+11

𝑥+4 .

1. Use the rational zero theorem to find all possible rational zeros of the function

𝑓(𝑥) = 𝑥4 + 5𝑥3 − 11𝑥2 + 15𝑥 − 42 Then completely factor the function into a set of 𝑥 ± 𝑛 binomials.

1. We can roughly model the altitude of a vertically-launched unpowered projectile with the formula 𝑎 = −32𝑡2 + 𝑣𝑡 where 𝑣 is the initial speed of the projectile in feet per second.

Young Achilles, the ancient Greek hero, is playing around after archery practice one day and shoots an arrow straight up. (Note: Do not try this at home.) The arrow leaves his bow at a speed of 240 feet per second. Find the time that the arrow is in the air and the maximum altitude it reaches. You may wish to visually represent this function as a parabola comparing altitude and time. (Disregard air resistance and the fact that the arrow is about seven feet off the ground when it is launched.)