Algebra 2 Problems of the Day (Jan 2020)

Daily Algebra 2 questions and answers.

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January 2020, Part II

All Questions in Part II are worth 2 credits. Work must be shown. Partial credit is given.


27. Describe the transformation applied to the graph of p(x) = 2^x that form the new function q(x) = 2^{x - 3} + 4

Answer:
The graph would shift 3 units to the right and 4 units up.

More info:
The + 4 is a vertical move. Whatever calculations are done involving x, they have been completed by the time the 4 is added, so the shift is vertical.

Changing 2^x to 2^{x - 3} means that the new function will have lower exponent values. It won't rise to the same level until the input is 3 higher. That is, 3 to the right, not the left.

You can graph the two functions in your calculator to see the difference. You can sketch them on the paper, if you want, but it isn't necessary. You just need to describe the transformation.

28. The parabola y = - 1/20(x - 3)² + 6 has its focus at (3,1). Determine and state the equation of the directrix.
(The use of the grid below is optional.)

Answer:
The parabola has its vertex at (3, 6), which we know because it's written in vertex mode.
The vertex is the midpoint between of a line between focus and directrix.
6 - 1 = 5
6 + 5 = 11
The equation for the directrix is y = 11.

Comments and questions welcome.

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