Lesson 2: Square Root Method
Find the roots of equations



Unit 5 Study Guide
How did you determine the solutions to a quadratic equation written in this format?
What was your justification for each step?
How can you recognize when to use the square root method?
Lesson 3: Factored form
Find the roots of each by factoring



How does factoring help with finding solutions to a quadratic equation?
What methods can you use to factor quadratic equations from standard form?
Are there quadratic equations that cannot be factored? Why or why not?
Lesson 4: History and Houses (Word Problems)



How are quadratic equations useful for real-world situations?
What types of solutions are best suited for using quadratic models?
Which solving method did you find yourself using the most?
Lesson 5: Completing the Square
Solve each quadratic equation by completing the square
Rewrite the equation in vertex form by completing the square
x2−6x+6=0
 What step was the hardest in the process of completing the square?
 Can you explain your process for putting the expression in vertex form/



Explain your thinking for each step.
What factor in the original expression made it easy to complete the square/
For what type of quadratic equations is completing the square useful?
Lesson 6: The Quadratic Formula
Solve each using the quadratic formula




Do you know the quadratic formula?
What form does a quadratic formula need to be before you use the quadratic
formula?
Is the quadratic formula the fastest/easiest way to solve quadratic equations?
When is the quadratic formula useful?
Lesson 7: Area and Perimeter
Find the dimensions of each rectangle



Which methods for solving quadratics did you use most and why?
What does your answer mean in terms of the problem’s context?
Was there ever a quadratic that you set up that had more than two solutions? What
does that mean?
Lesson 8: Using the Discriminant
Without finding the zeros, specify the number of solutions each equation will have


What part of the quadratic equation is the discriminant?
How does the discriminant indicate the number of solutions to a quadratic
equation?
 What values of the discriminant indicate two, one, or no real solutions?
Lesson 9: Discriminant and Graphs
Use the discriminant to match each of the equations with the graphs shown below


How are the discriminants and the graphs of quadratic equations linked?
How do the discriminant and the graph each show the solutions to a quadratic
equation?
 How do you find the solution set when you set two functions equal to each other (ex
F(x)=G(x))?
Lesson 10: The Rock Concert
If a toy model 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 equation h(t)=16t2+128t.
a. How long will it take the rocket to return to the ground?
b. After how many seconds will the rocket be 112 feet above the ground?
c. How long will it take the rocket to hit its maximum height?
d. What is the maximum height?
e. Sketch a graph of the rocket’s trajectory.
 How can you use functions and equations to solve word problems?
 What methods did you use to solve the word problems?
4.
5.
1
6.
16
6.
49
Get Initials or Loose ALL Credit
Set B
Lesson
Real to Complex
Simplify14:
theFrom
radical.
Simplify the radical
7.
8.
20
7.
9.
75
8.
50
9.
10.
10.
11.
18
12.
96
150
11.
12.
SetWhat
is an imaginary number?
C
 What is a complex number?
Simplify
How are
the complex
radical. numbers useful for solving quadratics?
Get Initials or Loose ALL Credit
 What do complex numbers allow you to express?
2
Lesson
Solving
Quadratic
13. 15: 27a
14. Equations
16c2d2
15.
50x2 yz3
13.
Solve the quadratic equations using any method you like. If you get a complex solution,
14.
make sure you show the complex solution using i.
15.
16.
9 10
320y z
17.
64x
4
18.
4 2
100a b
16.
17.
18.
19.



3 5
56a b
20.
3 6
125x y
21.
7 8
150x y
19.
20.
When do quadratic equations have complex solutions?
21.
Can quadratic equations have both real and complex solutions?
What method can you use to determine if the solutions will be real or complex?
Get Initials or Loose ALL Credit