algebra quiz help

Quiz 4 - SPRING 2016 - MATH 107 - COLLEGE ALGEBRA

Problem 1:

Find all real number solutions to the following equation:

5 − (2x − 1)2 = 0

Problem 2:

Find all real number solutions to the following equation:( x−

1

2

)2 =

3

4

Problem 3:

Perform the indicated operations

(1 − 3i) − (4 + i)

Problem 4:

Find the complex solutions to the following equation1:

x4 −x2 − 2 = 0

1Remember, all real numbers are complex numbers, so complex solutions means both real and non-real

answers.

Quiz 4 - SPRING 2016 - MATH 107 - COLLEGE ALGEBRA

Problem 5:

Graph the following functions starting with the graph of f(x) = x2 and using transfor-

mations. Find the vertex, state the range and find the x− and y−intercepts, if any exist.

g(x) = (x− 2)2 − 1

Problem 6:

Convert the functions below from general form to standard form. Find the vertex, axis

of symmetry and any x− or y−intercepts. Graph the function and determine its range.

f(x) = x2 − 6x + 5

Problem 7:

Let f(x) = 2x + 1 and g(x) = 7

a) Solve f(x) = g(x)

b) Solve f(x) < g(x)

c) Solve f(x) > g(x)

d) Graph y = f(x) and y = g(x) on the same set of axes and interpret your solutions to

parts a through c above

Problem 8:

Solve the following inequality analytically; check your answers graphically:

|x− 2| ≥ 3

SPRING 2016 - MATH 107 - COLLEGE ALGEBRA

Quiz 4 - SPRING 2016 - MATH 107 - COLLEGE ALGEBRA

Problem 9:

Find the quadratic regression, and graph both the scatter plot and the quadratic regres-

sion, for the following set of data:

x 1 2 3 4 5 6 7 8 9

y 1.390 1.634 5.900 9.069 16.878 25.763 37.531 50.590 64.374

Problem 10:

Find the quadratic regression, and graph both the scatter plot and the quadratic regres-

sion, for the following set of data:

x 1 2 3 4 5 6 7 8 9

y -2.602 0.782 1.919 0.094 -3.723 -8.701 -15.485 -23.319 -35.491

SPRING 2016 - MATH 107 - COLLEGE ALGEBRA