PRECALCULUS PRACTICE WORKSHEET

Problem 1 :

Find the product and write the result in standard form.

(8 – 3i) (-2 – 3i)

Solution

Problem 2 :

Divide and express the result in standard form.

58 - i

Solution

Problem 3 :

Solve the quadratic equation using the quadratic formula. Express the solution in standard form.

4x2 – 3x + 1 = 0

Solution

Problem 4 :

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

f(x) = 5x2 + 10x - 5

Solution

Problem 5 :

Solve the problem.

The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function

C(x) = 5x2 – 20x + 36

Find the number of automobiles that must be produced to minimize the cost.

Solution

Problem 6 :

Find the zeros of the polynomial function.

f(x) = x3 + 4x2 – 4x - 16

Solution

Problem 7 :

Divide using long division or synthetic division

3m2+18m2 - 74m + 63 m + 9

Solution

Problem 8 :

Find a rational zero of the polynomial function and use it to find all the zeros of the function.

f(x) = x3 – 8x2 + 19x - 14

Solution

Problem 9 :

Find the domain of the rational function.

h(x) = x + 2x2 - 49x

Solution

Problem 10 :

Find the vertical asymptotes, if any, of the graph of the rational function.

x - 64x2 - 15x + 54

Solution

Answer Key

1)  -25 - 18i

2)   8/13 + (1/13)i

3)  

4)  (-1, -10).

5) the required the number of automobiles is 2000.

6)  x = -2, x = 2 and x = -4

7)  3m2 - 9m + 7 = 0

8)  x = 2, x = 3 + √2 and x = 3 - √2

9)  (-∞, 0) ∪ (0, 49) ∪ (49, ∞)

10)  So, vertical asymptotes are x = 6, x = 9

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