Understanding the Quadratic Equation: Simplifying y = 3(2)² – 12(2) + 15 Step by Step

Solving quadratic equations is a foundational skill in algebra, and one that often causes confusion—even for experienced learners. In this article, we break down the equation:

y = 3(2)² – 12(2) + 15
and simplify it step by step to reveal why it finally simplifies to y = 3. Whether you're studying algebra, teacher, or self-learner, understanding how to evaluate and simplify expressions—especially quadratic forms—is essential for mastering more complex math concepts.

Understanding the Context

What Is the Given Equation?

Our starting equation is:
y = 3(2)² – 12(2) + 15

At first glance, this seems like a standard quadratic expression—but in this case, we’ll treat it like a linear evaluation problem since no variable “y” is isolated as the subject. But the challenge lies not in solving for a variable, but in correctly evaluating the expression using order of operations (PEMDAS/BODMAS).

y = 3(2)^2 - 12(2) + 15 = 12 - 24 + 15 = 3

Key Insights

Step 1: Apply the Exponent First

Because of the exponent (2) in (2)², we apply the P (Parentheses) rule in sequence with E (Exponents):
(2)² = 4

Now substitute:
y = 3 × 4 – 12 × 2 + 15

🔗 Related Articles You Might Like:

📰 Inside How One Garage Turned a Broken F150 Into a Legend—Check Click Fast! 📰 Would USC Law’s New 247 Rule Break a Shocking Secret No One’s Talking About 📰 What USC 247 Exposes That Could Rewrite College Sports Forever 📰 Die Lsungen Sind X 3 Und X 1 📰 Die Lsungen Sind 📰 Die Rckfahrt Dauert 2 Stunden Und 15 Minuten 📰 Die Volumenformel Fr Eine Kugel Lautet V Frac43Pi R3 📰 Die Volumenformel Lautet V Textlnge Times Textbreite Times Texthhe 📰 Diese Einfachen Katzen Zeichnungen Bringten Mich Zum Lachen So Einfach Du Auch 📰 Diesel Engine Failure These Ship Parts Will Save Your Voyage Senatorshidden 📰 Dire Intense And Hyper Focused On Transformation And Gameplay Thrills 📰 Disaster Watch These 5 Shuffled Anime Shots Will Leave You Speechlessshocking Reveals Inside 📰 Disasterpony Shota Hentai Lost Fans Crave These Forbidden Moments Absolute Truths Revealed 📰 Discount Shotas Mastery Top 10 Hacks That Made Him Unstoppable 📰 Discounted So3 Lewis Structure Secrets Why Its Not Just A Simple Molecule 📰 Discover Everything You Need In The Ultimate Skyrim Wiki Guide Dont Miss These Secret Secrets 📰 Discover Hidden Sims 4 Worlds These Secret Realms Will Change How You Play Forever 📰 Discover How Norrin Radds Silver Surfer Saga Stuns Fans Around The Universe

Final Thoughts

Step 2: Perform Multiplication from Left to Right

Multiplication comes before addition and subtraction, per BODMAS/PEMDAS:

First term: 3 × 4 = 12
Second term: 12 × 2 = 24

Now substitute:
y = 12 – 24 + 15

Step 3: Evaluate from Left to Right (Addition and Subtraction)

We proceed left to right:

12 – 24 = –12
Then: –12 + 15 = 3

Final Result:

y = 3