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Unit 4 Study Guide (Due 2/3/2026)

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Last updated about 2 hours ago
40 questions
Required
10
Required
10
Required
10

Day 1 (1/30/26)

Imaginary Numbers

Required
10
Question 1
1.

Match the each power of i to its correct expression.

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Question 2
2.

Match the each power of i to its correct expression.

Draggable itemarrow_right_altCorresponding Item
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Question 3
3.
Simplify this radical. (Don't forget to split your answer into two parts.)

1st Solution
_______
2nd Solution
_______
Question 4
4.
Simplify this radical. (Don't forget to split your answer into two parts.)

1st Solution
_______
2nd Solution
_______

Finding Products involving i

Required
10
Question 5
5.

Simplify each expression.

Required
10
Question 6
6.

Simplify each expression.

Adding and Subtracting Complex Numbers

Required
10
Question 7
7.

Simplify each expression. Final answers must be in a + bi form.

Required
10
Question 8
8.

Simplify each expression. Final answers must be in a + bi form.

Multiplying Complex Numbers

Required
10
Question 9
9.

Simplify each expression. Final answers must be in a + bi form.

Required
10
Question 10
10.

Required
10

Solve by Square Root Property

Required
20
Question 12
12.
Solve using the square roots method. Write the answer in simplest form.

Solution 1_______
Solution 2 _______
Required
10
Required
20
Required
10
Required
10
Required
10
Required
20
Required
20
Required
20
Required
20

Day 2 (2/2/26)

Finding Discriminants


Required
10
Question 22a
22a.

Determine the discriminant of the following quadratic:


Required
10
Question 22b
22b.

Finding the discriminant

Required
10
Question 24a
24a.

Required
3
Required
0
Required
20

Finding the discriminant

Required
10
Question 25a
25a.

Required
3
Required
0
Required
20

Solving Quadratic Equations with Complex Solutions with the Quadratic Formula



Required
30
Question 26
26.
Required
30
Required
30

Solve using the Quadratic Formula

Quadratic Equation Word Problems

Required
20
Question 29
29.
Required
20
Required
30
Required
30
Simplify each expression. Final answers must be in a + bi form.
Question 11
11.

Simplify each expression. Final answers must be in a + bi form.

Question 13
13.
Solve each Quadratic Equation (Don't use the variable in your answer.)


1st solution_______

2nd solution_______
Question 14
14.
Solve using the square roots method. Write the answer in simplest form.

Solution 1_______
Solution 2 _______

Completing the Square

Question 15
15.
Rewrite the equation by completing the square.

3x² -12x + 15= 0

First you need to divide the left side and the right side by _______.

What is the new middle term?_______

Now move the constant term by _______ to both sides of the equation.

So now you have _______

Now take half of the coefficient of the new middle term and combine it with x inside the parentheses to create a perfect square trinomial on the left and square it and add it to the right side.

(x _______ )² = _______
Question 16
16.
Rewrite the equation by completing the square.

x² + 6x = 0

can be rewritten as

(x _______ )² = _______
Question 17
17.
Rewrite the equation by completing the square.

x² -10x = 0

can be rewritten as

(x _______ )² = _______
Question 18
18.
Solve using the square roots method. Write the answer in simplest form.

Solution 1_______
Solution 2 _______
Question 19
19.
Solve using the square roots method. Write the answer in simplest form.

Solution 1_______
Solution 2 _______
Question 20
20.
Solve each Quadratic Equation by Completing the Square (Don't use the variable in your answer.)

1st solution_______

2nd solution_______
Question 21
21.
Solve each Quadratic Equation by Completing the Square (Don't use the variable in your answer.)

1st solution_______

2nd solution_______
Because the value of the discriminant was __________, that means the quadratic equation will have ____________________ solutions.
Required
10
Question 23a
23a.

Determine the discriminant of the following quadratic:

Required
10
Question 23b
23b.
Because the value of the discriminant was __________, that means the quadratic equation will have ____________________ solutions.
Determine the discriminant of the following quadratic:

Question 24b
24b.
Because the value of the discriminant was __________, that means the quadratic equation will have ____________________ solutions.
Question 24c
24c.
The best way to solve this quadratic equation is to __________
Question 24d
24d.
Solve this Quadratic Equation using the quadratic formula:


Remember that you already converted this into Standard Form

solution 1
x=_______
solution 2
x=_______
Determine the discriminant of the following quadratic:

Question 25b
25b.
Because the value of the discriminant was __________, that means the quadratic equation will have ____________________ solutions.
Question 25c
25c.
The best way to solve this quadratic equation is to __________
Question 25d
25d.
Solve this Quadratic Equation using the quadratic formula:


Remember that you already converted this into Standard Form

solution 1
x=_______
solution 2
x=_______
Solve this Quadratic Equation using the quadratic formula:



Put this equation in Standard Form:
_______

Find
a=_______
b=_______
c=_______


solution 1
x= _______
solution 2
x=_______
Question 27
27.
Solve this Quadratic Equation using the quadratic formula:


Put this equation in Standard Form:
_______

Find
a=_______
b=_______
c=_______
solution 1
x=_______
solution 2
x=_______
Question 28
28.
Solve this Quadratic Equation using the quadratic formula:



a=_______
b=_______
c=_______
solution 1
x=_______
solution 2
x= _______
Solve this Real World Quadratic Equation word problem. Pick any method to solve.

The length of a rectangle is 3 more than the width. If the area is 40 square inches, what are the dimensions?

Length_______

Width_______
Question 30
30.
Solve this Real World Quadratic Equation word problem. Pick any method to solve.

The length of a rectangle is 4ft greater than the width. If each dimension is increased by 3, the new area will be 33 square feet larger. Find the dimensions of the original rectangle.

Length_______

Width_______
Question 31
31.
Solve this Real World Quadratic Equation word problem. Pick any method to solve. Round your answer to the nearest tenth.

A ball is thrown into the air by a person. Its height above the ground, h (measured in feet), at any given time after the ball is thrown, t (measured in seconds), can be modelled using the quadratic function h(t) = -16t² + 16t + 5.


From what height is the ball thrown?_______

When did it hit the ground?_______

What is the ball's maximum height?_______
Question 32
32.
Solve this Real World Quadratic Equation word problem. Pick any method to solve. Round your answer to the nearest tenth.

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equations h(t) = -16t²+ 128t (if air resistance is neglected).


How long will it take for the rocket to return to the ground? _______
What is the ball's maximum height?_______

How long will it take the rocket to hit its maximum height?_______