3.1 - 3.4 Review_Alg2

3.1 - 3.4 Review

3.1 Solving Quad Equations

3.2 Complex Numbers

3.3 Completing the Square

3.4 Quadratic Formula

3.1 Solving Quadratic Equations

Solve by Graphing, Algebraically, and by Factoring

Or...

The other way I showed you in class is to type y = 0 into Y₂, hit 2nd, trace, 5: intersect, and then hit enter 3 times. That will also give you the x-intercepts or the solutions. I couldn't find a video that showed that I can't upload my own videos to Quizizz. Sorry!

Multiple Choice

Determine the solutions of the graph:

• No real solutions

• x = -3 or x = -1

• Infinity Many Solutions

• x = -1

Multiple Choice

Solve the equation by graphing: $-x^2-7x-6=0$   

•  $x=1\ and\ x=6$  

•  $x=-6$  

•  $x=-6\ and\ x=-1$  

• No Solutions

Multiple Choice

2x²=100

• x = √25
• x = ±5√2
• x = √100
• x = ±√5

Multiple Choice

(x + 3)² = 36

• x = √36
• x = √39
• x = -9 and x = 3
• x = 9 and x = -3

Multiple Choice

What are the roots of quadratic equation 

 $x^2-49=0$  ?

•  $\pm7$  

•  $\pm1$  

•  $\pm8$  

•  $\pm4$  

Multiple Choice

Solve by factoring:  $x^2-9x+20=0$  What does the factoring step look like?

•  $\left(x-4\right)\left(x+5\right)=0$  

•  $\left(x+20\right)\left(x-9\right)=0$  

•  $\left(x-4\right)\left(x-5\right)=0$  

•  $\left(x+4\right)\left(x+5\right)=0$  

Multiple Choice

Solve by factoring:  $x^2-9x+20=0$  

• x = - 4 and x = - 5

• x = 20 and x = - 9

• x = 4 and x = 5

• x = - 4 and x = 5

Multiple Choice

What is the factored form of  $4x^2+4x+1=0$  ?

•  $\left(2x+1\right)\left(2x+1\right)=0$  

•  $\left(2x-1\right)\left(2x+1\right)=0$  

•  $\left(2x-1\right)\left(2x-1\right)=0$  

•  $\left(4x+1\right)\left(1x+1\right)=0$  

Multiple Choice

What is the solution for  $4x^2+4x+1=0$  ?

•  $x=\frac{1}{2}or\ x=-\frac{1}{2}$  

•  $x=-\frac{1}{2}$  

•  $x=\frac{1}{2}$  

•  $x=\frac{1}{4}or\ x=1$  

3.2 Complex Numbers

Find square root of negative numbers, Operations with complex numbers, Solve quad equation with complex solutions

Multiple Choice

What are the zeros of the function f(x) = x² + 64?

• -8 and 8
• -8i and 8i
• (-√8) i and (√8) i
• -√8  and √8

Multiple Choice

Solve the equation $3x^2+96=0$  

•  $\pm4\sqrt{2}$  

•  $\pm4i\sqrt{2}$  

•  $2i\sqrt{4}$  

•  $\pm2\sqrt{4}$  

Multiple Choice

What does i² = ?

• -1
• √-1
• 1
• -√1

Multiple Choice

Find the sum.
(5-2i) + (-7+8i)

• -2+6i
• 12+6i
• -35-16i²
• -35 -16i

Multiple Choice

The product of (3 -2i) and (7+6i) is

• 21 - 12i
• 9 + 4i
• 33 + 4i
• 21 + 16i

Multiple Choice

(7 - 5i)(7 + 5i)

• 74
• 24
• 49 - 25i
• 49 + 25i

3.3 Completing the Square

Solve quad equations by completing the square, Write quad functions in vertex form

Multiple Choice

Solve by completing the square.
x² +12x = 5

• X = 6 + √41 or  6 − √41
• X= 35 or 47
• X = −6 + √41 or  −6 − √41
• X = √35 or √47

Multiple Choice

Complete the Square
x² + 6x = 5

• (x + 3)² = 5
• (x + 6)² = 9
• (x + 3)² = 14
• (x + 6)² = 14

Multiple Choice

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

• 4
• 2
• 8
• 20

Multiple Choice

Find the missing value "c" to complete the square.

x² + 6x + ____

• 9

• 12

• 36

• - 9

Multiple Choice

Complete the Square and write in Vertex Form:

f(x) = x² + 6x + 5

• (x + 3)² - 4

• (x + 6)² - 4

• (x + 3x)² - 4

• (x + 3)² + 9

Multiple Choice

Complete the Square and write in Vertex Form:
f(x) = x² + 6x + 5

• (x + 3)² - 4
• (x + 6)² - 4
• (x + 3x)² - 4
• (x + 3)² + 9

3.4 Using the Quadratic Formula

Solve quad equations with the quadratic formula

Use the discriminant to determine solutions

Multiple Choice

Determine the values of
a, b, and c for
the quadratic equation: 
4x² – 8x = 3

• a = 4, b = -8, c = 3
• a = 4, b =-8, c =-3
• a = 4, b = 8, c = 3
• a = 4, b = 8, c = -3

Multiple Choice

Solve Using the Quadratic Formula

2x² + 7x - 15 = 0

• -1.5 or 5

• No Solution

• -5 or 1.5

• 0.7 or 5

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Solve the quadratic equation using the quadratic formula.

2x² - x + 3 = 0

• $x\ =\ \frac{1}{4}\pm\frac{\sqrt{23}}{4}i$

• $x\ =\ \frac{1}{4}\pm\frac{5}{4}i$

• $x\ =\ -\frac{1}{4}\pm\frac{\sqrt{23}}{4}$

• $x\ =\ -\frac{1}{4}\pm\frac{5}{4}i$

• $x\ =\ \frac{3}{4}\ \ or\ \ x\ =\ -\frac{7}{4}$

Multiple Choice

Solve Using the Quadratic Formula

2x² + 7x - 15 = 0

• -1.5 or 5

• No Solution

• -5 or 1.5

• 0.7 or 5

Multiple Choice

The discriminant is

• aX² + bX + c

• b - 4ac

• b² - 4ac

• b² + 4ac

Multiple Choice

What is the discriminant and how many solutions would this quadratic have?

-8x² + 6x - 4 = 0

• -92, 2 Imaginary Solutions

• 164, 2 Real Solutions

• -164, 2 Imaginary Solutions

• 92, 1 Real Solution

Multiple Choice

What is the discriminant and how many solutions would this quadratic have?

x² - 6x + 9 = 0

• 0, 2 Imaginary Solutions

• 0, 1 Real Solution

• 72, 2 Real Solutions

• -72, 2 Imaginary Solutions

Multiple Choice

Determine the value of the discriminant and name the nature of the roots for the following:

x² + 7x + 13

Remember: b² - 4ac

• 400, 2 real solutions

• 0, 1 real solution

• -400, 2 imaginary solutions

• -3, 2 imaginary solutions