Solution: Given $ p(y) = y^2 - 6y + 9m $ and $ p(5) = 22 $, substitute $ y = 5 $: - Decision Point
Solving $ p(y) = y^2 - 6y + 9m $ Using the Given Condition $ p(5) = 22 $
Solving $ p(y) = y^2 - 6y + 9m $ Using the Given Condition $ p(5) = 22 $
When solving for unknown parameters in quadratic functions, substitution is one of the most effective techniques. In this article, we explain the step-by-step solution to determine the value of $ m $ in the function $ p(y) = y^2 - 6y + 9m $, using the condition that $ p(5) = 22 $.
Understanding the Context
Step 1: Substitute $ y = 5 $ into the function
Given:
$$
p(y) = y^2 - 6y + 9m
$$
Substitute $ y = 5 $:
$$
p(5) = (5)^2 - 6(5) + 9m
$$
Image Gallery
Key Insights
Step 2: Simplify the expression
Compute each term:
$$
p(5) = 25 - 30 + 9m
$$
$$
p(5) = -5 + 9m
$$
Step 3: Apply the given condition
We’re told that $ p(5) = 22 $. So:
$$
-5 + 9m = 22
$$
🔗 Related Articles You Might Like:
📰 coding post 📰 codorus state park 📰 codpiece 📰 The Real Jschlatt Behind The Name The Secrets The Untold Truth 4980904 📰 You Wont Believe The Average Annual Salary In The Usbroke Or Beam Break It Down Now 1272452 📰 April Weather In London Uk 8410738 📰 Will Lawyers Near Me 5486482 📰 How To Master Full Edit Mode In Sims 4 You Wont Believe What You Can Change 4278466 📰 5 So Addictive Its Unreal The Series That Transformed How The World Handles Anger 9394363 📰 5A Perfect Blend Of Cuteness Dramapet Girl Of Sakurasou Explodes In Viral Content 81084 📰 The Nave Truth About Average Mens Foot Sizeconsequences You Need To Know 4577451 📰 You Wont Believe Whats Happening On Stockxs Dark Side 1355030 📰 Why Varian Tangled Became First Choice For Fans Of Boundless Drama Thrills 2579922 📰 R Programming Language 6425256 📰 Timer Roblox 8009570 📰 Appdata Secrets Exposed This Hidden Folder Could Be Threatening Your Privacy Forever 860771 📰 Kohberger Family 6031906 📰 A Piece Of Wire 24 Meters Long Is Cut Into Two Pieces One Piece Is Bent Into A Square And The Other Into A Circle If The Squares Perimeter Is Equal To The Circles Circumference What Is The Length Of Wire Used For The Square 916863Final Thoughts
Step 4: Solve for $ m $
Add 5 to both sides:
$$
9m = 27
$$
Divide by 9:
$$
m = 3
$$
Final Result
The value of $ m $ that satisfies $ p(y) = y^2 - 6y + 9m $ and the condition $ p(5) = 22 $ is:
$$
oxed{3}
$$
This method is essential in algebra for diagnosing quadratic functions and solving for parameters directly from function values — a key skill in school math and standardized problem-solving.
