Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

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June 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.


4. The expression 6xi³(-4xi + 5) is equivalent to
1) 2x - 5i
2) -24x² - 30xi
3) -24x² + 30x - i
4) 26x - 24x²i - 5i

Answer: 2) -24x² - 30xi
i² = -1, i³ = -1i = -i, i⁴ = i²i² =(-1)(-1) = 1

6xi³(-4xi + 5)
-24x²i⁴ + 30xi³
-24x²(1) + 30x(-i)
-24x² - 30xi

5. If f(x) = 3|x| - 1 and g(x) = 0.03x³ - x + 1, an approximate solution for the equation f(x) = g(x) is
1) 1.96
2) 11.29
3) (-0.99, 1.96)
4) (11.29, 32.87)

Answer: 2) 11.29
Eliminate choices 3 and 4 because the solution is a single number, not an ordered pair.
There are up to three possible intersections. If you graph them, you will find them at approximately -0.99, 0.5, and 11.29.

6. Given the parent function p(x) =cos x, which phrase best describes the transformation used to obtain the graph of g(x) = cos(x + a) - b, if a and b are positive constants?
1) right a units, up b units
2) right a units, down b units
3) left a units, up b units
4) left a units, down b units

Answer: 4) left a units, down b units
Inside the parentheses, plus shifts to the left and minus shifts to the right. Outside of the parentheses, plus moves the graph up and minus moves the graph down.

Comments and questions welcome.

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