# 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 3x^{2}+7x = 2 and x^{2}+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+y^{2} = 7.

4) Consider the curve y = x^{2}+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 = x^{2}−5x+7? of x^{2}+y^{2}
= 9? of y = 1/x

?

6) Why is

7) If f (x) = x^{2}+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+h^{2}.

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

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