1. Completely factor the following expressions (3pts each):

2. Given the general quadratic equation ax^2 + bx + c = 0 , state the Quadratic Formula (3pts):

3. Use the method of** COMPLETING THE SQUARE** to solve
the quadratic equations (4pts each)

4. Use the **QUADRATIC FORMULA** to solve the quadratic
equations: (4pts each)

5. Without actually solving the equation, use the
discriminant to discuss the nature of the roots of the following

quadratic equations (3pts each):

6. Solve the equation (**do not check for extraneous
solutions**): (4pts)

7. Solve the equation (**do not check for extraneous
solutions**): (4pts)

8. After doing everything correctly, Joe College

obtained x = 9/4 and x = 4 as solutions to the

equation . Determine which

solution(s) is (are) extraneous. (4pts)

9. After doing everything correctly, Joe College

obtained x = -5 and x = 3 as solutions to the

equation . Determine which

solution(s) is (are) extraneous. (4pts)

10. Shade the area of the plane determine by the following inequalities: (2pts each)

11. Solve the following systems of equations by using the
**SUBSTITUTION** method (4pts each):

12. Solve the following systems of equations by using the
**ELIMINATION** method (4pts each):

13. Determine an equation of a line which is parallel

to the line 2x + 3y = 27 and passing through the

point (3, -4). (4pts)

14. Determine an equation of a line which is

perpendicular to the line and passing

through the point (-3, 5) . (4pts)

15. Determine an equation of the perpendicular bisector of
the line segment whose midpoint is (−2,3) and has

slope = -7/4. (4pts)

16. Write an equation of a circle with center at. (3pts
each)

(a) (3, 4) and radius of 5

(b) (–2, 5) and radius of 7

17. Determine the center and radius of each of the circles (3pts each)

18. Sketch the graph of the circle with center at (3, 2) and radius = 5. (3pts)

19. Determine the center and radius of the circle (5pts).