Must show all work. There are 12 questions. Write work on separate piece of paper, put my name in top corner. If all work is not shown, payment will not be released.

Final Exam College Algebra Spring 2020

Name___________________________________

Unless otherwise noted each problem is worth 4 points. Show all Your work for full credit.

Solve the equation.

1) a)

(x – 3)2 = 25

b)

Solve the equation (any method).

2)

a) x2 + 4x – 3= 0

5x + 4 = -7

b) 2×2 = -5x – 7

1

Rationalize the denominator. Assume that all variables represent positive real numbers.

3

3

3) a)

b)

2

5+ 3

Indentify the vertex and Graph the parabola. Give the vertex, axis, domain and range.

4) a) f(x) = 2(x + 3)2 – 3

b) f(x) = -x2 + 4x – 3

Using a table graph the following function and give the domain and range.

5)

a) f(x) = 3x

2

b) f(x) = 3-x

Graph the given logarithmic function. Give the domain and range.

6) a) f(x) = log (x)

3

b) g(x) = log(x)

Solve the equation. Give exact and approximate answers to two decimal places.

7) (a) 10x = 85

(b)

5 (3x) = 125

8) Solve the logarithmic equation.

(a) log 7 (x) = 2

(b) log 3 (x-7 )= 2

Using the properties of logarithms write the following as the sum and/or difference of logarithms

9)

a)

ln (x 3 y5 )

b) log (

3

x2 y

)

w2z 3

Use properties of logarithms to write each expression as a single logarithm.

10) a)

log(x) – log(w)- log(z) + log(y)

b) 3 ln(x) -9 ln(y) – 5 ln(z)

Solve the problem.

11) A rocket is launched upward so that its distance (in feet) above the ground after t seconds is given by

h(t) = -11t2 + 286t. What is its maximum height and the number of seconds it takes to reach this height?

12) If an object is projected upward. Its height (in feet) is given by h(t) = -16t2 + 48t after time t seconds.

At what time or times will the object be 16ft from the ground? Aproximate your answers to two decimal places.

Hint: Use the Quadratic Formula

4