Methods of Solving Quadratic Equations

Presentation

•

Mathematics

•

9th Grade

•

Medium

•

CCSS

HSA-REI.B.4B, 8.EE.A.2

Standards-aligned

Gina Holdvogt

Used 24+ times

FREE Resource

13 Slides • 24 Questions

Methods of Solving Quadratic Equations

Goal: I can use the most efficient method to solve quadratic equations

Poll

Today, we are going to focus on solving quadratics using the three methods below. Which one do you feel most confident using?

Square Roots

Factoring

Quadratic Formula

Poll

Which method do you feel least confident using?

Square Roots

Factoring

Quadratic Formula

Reviewing Methods of Solving

We will use the next slides to refresh ourselves on each method. Then, we will determine which method is BEST to use.

Taking Square Roots

$ax^{2\ }+\ c\ =\ 0$ or $ax^{2\ }=\ c$ The equation is missing its "bx" term.
Isolate the $x^{2\ }$ term
Take the square root of both sides
Don't forget the +/-

Square Root Example

Multiple Choice

Solve by finding square roots and simplify completely:
$x^2-16=0$

$x=\pm16$

$x=4$

$x=\pm4$

No real solutions

Multiple Choice

Solve by finding square roots and simplify completely:

9k² = 225

x = 4

x=\pm4

$x=\pm25$

$x=\pm5$

Factoring

$ax^{2\ }+bx\ +c=0$
Must be in standard form and equal zero
If c term is missing ( $ax^2+bx$ ) , factor GCF
After factoring, set both factors equal to zero and solve for x.

Factoring Using GCF Example

Multiple Choice

Solve by factoring the GCF

10x^2-8x=0

$x=2;\ x=-\frac{5}{4}$

$x=2;\ x=\frac{5}{4}$

$x=0\ ;\ x=\frac{4}{5}$

$x=0;\ x=-\frac{4}{5}$

Factoring Trinomial Example

Multiple Choice

Solve by factoring:
$x^2+10x+24=0$

$x=6\ or\ x=4$

$x=\pm\sqrt{14}$

$x=-6\ or\ x=-4$

No real solutions

Quadratic Formula

Must be in standard form and set equal to zero
Used when the equation is NOT factorable
ALL equations can be solved using the quadratic formula

Quadratic Formula Example

Multiple Choice

Use the quadratic formula to find the solutions for

2x² - 9x + 5 = 0

x = -8.14 and x= 6.14

x = -4.07 and x= 3.07

x = 3.85 and x = 0.65

ZERO solutions

Which method should I use?

Certain equations can be solved using multiple methods. Others can only be solved one way.

Multiple Choice

Solve x² - 3x - 4 = 0 using any method.

x = 4 and -1

x = -4 and -1

x = 4 and 1

x = -4 and 1

Poll

Which method did you use to solve x² - 3x - 4 = 0 ?

Square Roots

Factoring

Quadratic Formula

Multiple Choice

Solve using any method

16a² - 9 = 0

a = ^-3/₄, ³/₄

a = ^-4/₃, ⁴/₃

a = ^-9/₁₆, ⁹/₁₆

a = ^-16/₉, ¹⁶/₉

Poll

Which method did you use to solve 16a² - 9 = 0 ?

Square Roots

Factoring

Quadratic Formula

Let's Determine the Most Efficient Methods

All these methods are great, but we need to know which ones work best for each equation.

Multiple Choice

Decide on the best method:

2x² - 7x + 2 = 0

Square Root Method

Factor Method

Quadratic Formula

Multiple Choice

Decide on the best method:

x² - 3x - 54 = 0

Square Root Method

Factor Method

Quadratic Formula

Multiple Choice

Decide on the best method:

4x² - 25 = 0

Square Root Method

Factor Method

Quadratic Formula

Solve the following questions using the most efficient method.

Multiple Choice

Solve using the method of your choice

x= -2, x= 4

x= -8

x =±8

x = -2.03 , x = 8.33

Multiple Choice

Solve using the method of your choice.

x= ±81

x= ±9

x= 4, x = 9

No solution

Multiple Choice

Solve using the method of your choice: x² - 8x = 20

x = 10 and x = -2

x = -10 and x = -2

x = 10 and x = 2

Multiple Choice

Solve by the method of your choice.

x= 4, x =-1

x=8/3, x= 9/5

x= 1/5, x= 3/7

x= 7, x= -2

Multiple Choice

Solve using the method of your choice: x² + 13x + 12 = 0

x = -12, -1

x = 12.03, 1.55

x = 13, 1

x = -13, -1

Multiple Choice

Solve using the method of your choice

2x² + 2x − 12 = 0

x = −2.67, 3.86

x = 2.67, 3.86

x = 2, −3

x = −2, −3

Multiple Choice

$x^2-7x=0$

Solve by the method of your choice.

x = 7 only

x = 0 only

x = 0 and 7

There is no real answer for this equation.

Multiple Choice

Solve using the method of your choice

9x² = 4 + 7x

x = 2 and x = 3

x = -1 and x = .25

x = 1 and x = -.45

x = 1.16, and x = -.38

Multiple Choice

Solve by the method of your choice

x = 5 , x = 7

x=2/3, x=6

x=4/7, x=6

x=-3/8, x = -7

Poll

How confident are you in your ability to solve quadratic equations using the method of your choice?

Not confident. I need more help.

Somewhat confident. I can do most but I struggle with a few.

Confident. I can do this on my own,

Very Confident. I could teach this to someone.

Methods of Solving Quadratic Equations

Goal: I can use the most efficient method to solve quadratic equations

Show answer

Auto Play

Slide 1 / 37

SLIDE

Similar Resources on Wayground

33 questions

Introduction to Functions

Presentation

•

8th - 9th Grade

33 questions

Continuous vs. Discrete

Presentation

•

9th Grade

36 questions

Exponent Rules

Presentation

•

8th - 9th Grade

35 questions

FUNGSI KUADRAT

Presentation

•

9th Grade

28 questions

8.5. Lesson 7- Compare Linear Functions

Presentation

•

8th Grade

29 questions

Factoring Review

Presentation

•

9th Grade

30 questions

Solving Quadratics by Square Roots

Presentation

•

9th - 10th Grade

30 questions

Topic 1 - equations & inequal. review

Presentation

•

9th Grade

Popular Resources on Wayground

10 questions

Safety Day 2026 – Student Review

Quiz

•

9th Grade

21 questions

Continents and Oceans

Quiz

•

6th Grade

20 questions

Parts of Speech

Quiz

•

5th Grade

16 questions

Subject & Predicate

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

12 questions

Map Skills

Quiz

•

3rd Grade

22 questions

Continents and Oceans

Quiz

•

5th Grade

15 questions

Rounding Decimals

Quiz

•

5th Grade

Discover more resources for Mathematics

12 questions

Absolute Value Equations

Quiz

•

9th Grade

20 questions

Function or Not a Function

Quiz

•

8th - 9th Grade

11 questions

Slope from 2 points

Quiz

•

8th - 9th Grade

10 questions

Exploring the Basics of Exponents

Interactive video

•

6th - 10th Grade

10 questions

Solving Absolute Value Equations

Quiz

•

9th Grade

18 questions

SB 12.2 Write in point slope form

Quiz

•

9th Grade

12 questions

Identify Rigid Transformations

Quiz

•

8th - 12th Grade

10 questions

Complementary, Supplementary, Vertical, and Linear Pairs

Quiz

•

9th - 12th Grade