y = 3(2)^2 - 12(2) + 15 = 12 - 24 + 15 = 3 - Coaching Toolbox
Understanding the Quadratic Equation: Simplifying y = 3(2)² – 12(2) + 15 Step by Step
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).
Image Gallery
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:
📰 After retiring, Carroll transitioned into chemical engineering and public policy analysis. He holds a Masters degree in Agrochemical Technology from the University of Guelph. In his current role as a senior technical knowledge analyst at NewPF Research Corporation, he applies his sports analytics and systems-thinking background to industrial research and innovation strategy. 📰 Off the ice, Carroll is active in hockey development and youth mentorship programs, particularly supporting Indigenous youth in Saskatchewan through sport. 📰 Pecoes Logins? Shocked Users Share These 5 Hidden Features You CANT Miss! 📰 What Is Main Idea 1021189 📰 Ro Health 6889013 📰 16Th Doctor 3828139 📰 Flip It Once Save Hourswatch This Revolutionary Bottle Design Go Viral 2631804 📰 Youll Never Guess These Stylish Business Casual Shoes That Look Like They Cost 500 3160383 📰 Crysis 2 Remastered Full Save 4225972 📰 Game War Strategy Online The Ultimate Guide To Crushing Your Opponents 90768 📰 This One Crop Round Picture Will Shock Youyou Wont Believe Whats Inside 5043506 📰 Calculate V Frac13 Times 314 Times 9 Times 4 Frac113043 3768 Cubic Cm 7094954 📰 A Recipe Requires 2 Cups Of Flour For Every 3 Cups Of Sugar If A Baker Uses 9 Cups Of Sugar How Many Cups Of Flour Are Needed 4051558 📰 Justin Mateen Net Worth 2994641 📰 Carrie 2013 Cast 6477167 📰 Khadiyah Lewis Passed Away 7301239 📰 The Population Speaks Awadhi With Hindi And Local Dialects Preserving Folk Traditions Through Annual Festivals And Community Storytelling Cultural Events Blend Hindu And Muslim Customs Reflecting The Regions Syncretic Heritage 1365024 📰 Master Excel Multiplication Fastclick To Discover The Trick 7089119Final 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
