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Algebra for Math 108

In Math 108, we will assume that you can handle the algebra of first and second degree polynomials with no problems
and without a calculator (except to decimalize your answers ). Here are examples of what we will assume you can
do. Do not ask yourself “Did I see this stuff before?” Instead ask “Can I work these problems right now?” If you are
not sure how to solve those problems right now, review the book’s first chapter ASAP, or enroll in Math 103 before
taking this course.

1) Solve 17x+25 = 16.

2) Use factoring or the quadratic formula

to solve quadratic equations such as 3x2+7x = 2 and x2+x = 6. You will be expected to have the quadratic formula
in your memory, and know how to use it.

3) Solve the system of equations

3x+4y = 6
x+y2 = 7.

4) Consider the curve y = x2+x. For which point(s) (x,y) on the graph of that curve will x = 5? For which point(s)
on the graph of that curve will y = 6?

5) What is the shape of the graph of y = x2−5x+7? of x2+y2 = 9? of y = 1/x
?

6) Why is

7) If f (x) = x2+3x, what is f (5+h)?

8) Where does the curve cross the x-axis?

**********

Solutions:
1) x = − 9/17
2) The solutions of the first quadratic equation are approximately x = -2.590667291 and x = 0.2573339576.
The solutions of the second equation are exactly x = −3 and x = 2.
3) The solutions are and x = −2,y = 3.
4) (5,30); (2,6)(−3,6)
5) parabola opening upward, circle with center at origin and radius 3, hyperbola
6) You cannot cancel that way. Instead

7) 40+13h+h2.

8) at x = 0 and x = 1/2

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