*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 x^{2} + 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.

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