Daily Regents: Maximum Values (August 2014)

I'll be reviewing a New York State Regents Exam Question every day from now until the Regents exams begin next month. At least, that is the plan.

August 2014, Questions 29

29. Let f be the function represented by the graph below. (See the image above). Let g be a function such that g(x) = -1/2 x² + 4x + 3.
Determine which function has the larger maximum value. Justify your answer.

The vertex of f(x) is (1, 6), so the maximum value of f is 6.

To find the vertex of g(x), first let's find the Axis of Symmetry, which runs through the Vertex. The formula for that is
x = -b / 2a
x = -(4) / ((2)(-1/2)). Note:: if you put this in your calculator, you need that "extra" pair of parentheses around the denominator.
x = -4 / -1 = 4

Find the value of g(4). This will be its maximum height. g(4) = -1/2(4)² + 4(4) + 3 = 11

Therefore, g(x) has a higher maximum value than f(x).

Any questions?

---

If anyone in Brooklyn is looking for an Algebra or Geometry Regents Prep tutor, send me a note. I have a couple of weekly spots available between now and June.