**Name:**

Show all work. How you get your answer is just
as important, if not more important, than the
answer itself. If you think it, write it!

- 1.
- (20 pts.) Find the equation of the line L which passes through the point (1,2) and is perpendicular to the line

Where does L hit the x-axis??

- 2.
- (14 pts.) What symmetries (x,y,origin), if any, do the graphs of the following functions/equations have??

(a) y = x^{4}-3x^{2}+17

(b) x^{2} + y^{3} = 5

(c) xy^{2} + yx^{2} = 1

- 3.
- (20 pts.) Find the standard form for the quadratic function

and use this information to sketch a graph of f. What is the lowest value that the function takes??

- 4.
- (15 pts.) Find an inverse of the polynomial function

(Hint: putting it in standard form, first, can help!). Be sure to describe what domain you pick to first make it one-to-one.

- 5.
- (15 pts.) Show that the polynomial function

has at least one root. Which two consecutive integers does your root lie in between?

- 6.
- (8 pts. each) For the polynomial function

use (synthetic or polynomial long) division to write f(x) as

(a) (x-2)g(x)+c

(b) (x+1)h(x)+d

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