# Math 2 Practice Problems for the Final

1. Solve the equation .

2. Perform the indicated ope rations and simplify completely .

3. Divide. (3x3 +12x − 4) ÷ (x − 2)

4. Use synthetic division . (x5 −1) ÷ (x −1)

5. Simplify.

6. Rationalize the denominator .

7. Solve by completing the square
a) 2x2 + 7x = 4
b) x2 + 6x + 2 = 0
c) x2 − 4x + 8 = 0
d) x2 + 5x = −7

8. Solve using the quadratic formula .
a) (x + 5)(x −1) = 2
b) 5x2 − 3 = 14x

9. Solve the system of equations

10. Graph the solution to the inequality in two variables (page 691):

11. Graph the solution to the system of inequalities (page 691):

12. Find the range of the quadratic function .
a) f (x) = 2x2 − 4x + 5
b) g(x) = −x2 + 6x +1

13. Graph the conic section :
a) x = −(y + 2)2 + 3
b) (x −1)2 + (y − 2)2 = 4
c) 4x2 + 4y2 +16x + 8y = 1

f) 6(x − 2)2 + 9(y + 5)2 = 36

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