Quadratic Formula Sums

Welcome to Algebra 1

Live Session 30:
I’m glad you are here!
Please make sure your desk/workspace is ready and read through the announcements.

Intro Question/Review of Last Session:
Solve the quadratic shown below:

0 = (𝑥+7)² -3

At Desk/Workspace:

● Pencil (preferred) or pen

● Paper

● Calculator

Agenda:

● Review

● Quadratic Formula

● Exit Ticket

Upcoming Assignments:
Studies: 11.3.1 Quizzes: 11.3.3
Checkup: 11.3.2

○
Remember to use reverse PEMDAS
method to solve

○
Start by moving the 3 to the left
side

○
Undo the exponent by taking a
square root on both sides,
remember that a square root can
be positive or negative!

○
Then subtract the 7.

Intro Question

Live Session #30

Learning Objectives:

●

Understand how and when to apply the quadratic formula.

●

Apply the quadratic formula to find the factors and roots of quadratic equations.

●

Calculate the discriminant of a quadratic equation and use it to determine the number of real roots.

●

Derive the quadratic formula.

Lessons Covered:

11.3 Quadratic Formula

Key Terms

Discriminant
Imaginary Number
Quadratic Formula

By the end of the lesson you should be able to define each word below.

●

Whenever we work with quadratic
expressions, we always label the
coefficients as a, b and c.

●

The quadratic term is labeled with a, the
linear term is labeled b, and the
constant term is labeled c (like shown
below)

●

𝑎𝑥²+ 𝑏𝑥 + 𝑐

Quadratic solutions

Multiple Choice

Identify a:

$$2x^2+4x+3=0$$  

• a = 4

• a = 3 

• a = 2 

• a = 1 

Multiple Choice

Identify b:

$$2x^2+4x+3=0$$  

• b= 4

• b= 3 

• b = 2 

• b = 1 

Multiple Choice

Identify c:

$$2x^2+4x+3=0$$  

• c= 4

• c= 3 

• c = 2 

• c = 1 

Multiple Choice

identify a:

$$-3x^2+5=4x$$  

• a = -3

• a = 5

• a = 4

• a = -4

Multiple Choice

identify b:

$$-3x^2+5=4x$$  

• b = -3

• b = 5

• b = 4

• b = -4

Multiple Choice

identify c:

$$-3x^2+5=4x$$  

• c = -3

• c = 5

• c = 4

• c = -4

Multiple Select

Identify a:  $$-x^2+4x+12=0$$   

• a = -1 

• a= 1 

• a = 4 

• a = 12

Multiple Choice

Identify b:  $$-x^2+4x+12=0$$   

• b = -1 

• b= 1 

• b = 4 

• b = 12

Multiple Choice

Identify c :  $$-x^2+4x+12=0$$   

• c= -1 

• c= 1 

• c = 4 

• c = 12

●

All quadratics have 2 solutions, those
followings can appear in any of the
combinations listed below:

○

2 unique real solutions (i.e. x = 7, x = -3)

○

2 non-unique real solutions (i.e. x = 7, x = 7)

○

2 complex solutions (i.e. x = 7i, x = -3i)

●

We can determine the type of solutions
a quadratic has with the formula

●

𝐷 = 𝑏²− 4𝑎𝑐.

Quadratic solutions

●

To find the discriminant:

○

Identify a, b, and c.

○

Substitute into equation and simplify.

○

Make conclusion on solutions.

■

Positive = 2 real

■

0 = 1 real

■

Negative = 2 Complex

●

Take 5 minutes to try and determine how many
solutions these quadratics have before checking
your answers.

Finding the Discriminant

Finding the Discriminant

Multiple Choice

The discriminant is

• aX²  + bX  +  c

• b - 4ac

• b² - 4ac

• b² + 4ac

Multiple Choice

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

• Positive

• Negative

• Zero

• Not Sure

Multiple Choice

What is the discriminant of -2x² − x − 1 = 0

• 76

• -7

• 9

• none of these

Multiple Choice

If the discriminant is positive, then the solution will be

• one real solution

• two real solutions

• no real solutions

• one imaginary solution

Multiple Choice

A function has a discriminant of 25.
______________
How many solutions does it have?

• 0
• 1
• 2
• 5

Multiple Choice

What are the roots of the function?

• x = 4, -1

• (-4, 1)

• x = -4, 1

• (4, 0) (-1, 0)

Multiple Choice

In the equation
y = x² +5x +7, match each leading coefficient with its correct letter 

• a=0, b=5, c=7

• a=1, b=5, c=7

• a=7, b=5, c=1

Multiple Choice

A function has a discriminant of -3.
______________
How many x-intercepts does it have?

• 0

• 1

• 2

• 3

Multiple Choice

____________
For the function above, is the discriminant positive, negative, or zero?

• Positive

• Negative

• Zero

• Not Sure

Multiple Choice

____________
For the function above, is the discriminant positive, negative, or zero?

• Positive

• Negative

• Zero

• Not Sure

Multiple Choice

How many solutions will this quadratic equation x²+8x+16 has?

• 2 real solutions

• 2 imaginary solution

• 1 solution

• 3 solutions

Multiple Choice

Given that the value of A=-5 , B=1 and C=-5, solve for the discriminant.

• -99

• 99

• 101

• -100

Multiple Choice

Solve for the discriminant of the given equation -2x² -6x=0

• -36

• 36

• 0

• 44

●

So far we have learned how to solve
quadratics using the following methods:

○

Factoring

○

Taking the square root on both sides

○

Completing the square

●

These methods only work on certain
types of quadratics and are not
guaranteed to work on all equations.
The only guaranteed method of solving
is the quadratic formula.

●

Given you have a quadratic in standard
form 𝑎𝑥²+ 𝑏𝑥 + 𝑐, the quadratic
formula is:

Quadratic Formula

●

Take notes on this quadratic formula
example:

●

Key Steps:

●

1) Make sure to set up the quadratic formula once
with a + sign and once with a – sign

●

2) Remember to solve the discriminant (part under
the square root) first

●

3) Be sure that you have 2 final answers

●

𝑥² + 2𝑥 + 1

Quadratic Formula

●

Take 5 minutes to use the quadratic formula to solve, then check your answers

9𝑛²= 4 + 7𝑛

5𝑥²− 4𝑥 + 6 = 0

Quadratic Formula

●

9𝑛²= 4 + 7𝑛

5𝑥²− 4𝑥 + 6 = 0

Quadratic Formula

Multiple Choice

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

• No Real Solution

Open Ended

$$2r^2+3r-1=0$$  

Solve using the quadratic equation.

Multiple Choice

$$2m^2=-2m+12$$   Solve using the quadratic formula.

• $$x=2,-3$$  

• $$x=3,-2$$  

• $$x=1\pm\sqrt{13}$$  

• No Solution

Multiple Choice

Solve using the quadratic formula...

9x² = 4 + 7x

• No solution

Multiple Choice

Solve using the Quadratic Formula.

• A

• B

• C

• D

Tips for Success

-Fill out the study guides 10.3.1 & 10.5.1

-Complete the checkups 10.3.2 & 10.5.2

-Complete the Practice 10.3.4 & Journal 10.5.4

-Complete Quizzes 10.3.3, 10.5.3

Exit Ticket

Solve the following quadratic using the quadratic formula.

Wrap-Up

If you have any questions or concerns about this course, please say behind so we can

chat!

Open Ended

Use the quadratic formula to solve the following:

6p² - 2p - 3

If you finish early...

• Complete 11.3.1 Study & 11.3.3 Quiz

• Complete 11.4.1 Study & 11.4.3 Quiz

• Work through any past missing work.​

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