Algebra 2 Problems of the Day

The following problems were taken from the ALGEBRA II (Common Core) Regents Exam given on Friday, January 27, 2017.
Previous problems can be found here

Part 1

11. The solution to the equation 18x² - 24x + 87 = 0 is

(4) (see image)

Follow along with the image. First, note that all the numbers are multiples of 3, so we can factor the equation by 3, allowing us to deal with some smaller numbers.
This makes a = 6, b = -8 and c = 29. You can do this with the larger numbers, too, and you should get the same answer.
Substitute the numbers into the Quadratic Formula and simplify, using the Order of Operations.
Once you get the discriminant = -632, you know that you have an imaginary answer. From the choices, you know that you will have 158 in the answer, and 632 / 158 = 4, which is a perfect square.
Note: At this point, you don't actually have to solve this. As you continue, you will likely be able to eliminate the three wrong choices. You can see that (8 + 2i) / 12 can only reduce to choice (4).

12. When g(x) = 2 / (x + 2) and h(x) = log(x + 1) + 3 are graphed on the same set of axes, which coordinates best approximate their point of intersection?

(2) (-0.9,1.9)
Put the equations into the graphing calculator and hit Graph. Next use "2nd" and "Trace" to get the Calc menu.
Select option 5, Intersection. Hit "ENTER" three times.
The x-coordinate is approximately -0.9269206, which rounds to -0.9.
The y-coordinate is approximately 1.863795, which rounds up to 1.9.




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