Solution: The maximum height occurs at the vertex. For $ y = -x^2 + 6x - 8 $, $ a = -1 $, $ b = 6 $, so $ x = -\frac62(-1) = 3 $. Substitute $ x = 3 $: $ y = -(3)^2 + 6(3) - 8 = -9 + 18 - 8 = 1 $. The maximum height is $ 1 $ unit. \boxed1

Solution: The maximum height occurs at the vertex. For $ y = -x^2 + 6x - 8 $, $ a = -1 $, $ b = 6 $, so $ x = -\frac62(-1) = 3 $. Substitute $ x = 3 $: $ y = -(3)^2 + 6(3) - 8 = -9 + 18 - 8 = 1 $. The maximum height is $ 1 $ unit. \boxed1 - Imagemakers

Understanding the Maximum Height of a Parabola: A Step-by-Step Solution

📅 May 3, 2026 👤 scraface

May 03, 2026

Understanding the Maximum Height of a Parabola: A Step-by-Step Solution

When analyzing quadratic functions, one essential concept is identifying the vertex, which represents the maximum or minimum point of the parabola. In cases where the parabola opens downward (i.e., the coefficient of $x^2$ is negative), the vertex corresponds to the highest point — the maximum height.

This article walks through a clear, step-by-step solution to find the maximum value of the quadratic function $ y = -x^2 + 6x - 8 $.

Understanding the Context

Step 1: Recognize the Standard Form

The given quadratic equation is in standard form:

$$
y = ax^2 + bx + c
$$

$Solution: The maximum height occurs at the vertex. For $ y = -x^2 + 6x - 8 $, $ a = -1 $, $ b = 6 $, so $ x = -\frac{6}{2(-1)} = 3 $. Substitute $ x = 3 $: $ y = -(3)^2 + 6(3) - 8 = -9 + 18 - 8 = 1 $. The maximum height is $ 1 $ unit. \boxed{1}$

Key Insights

Here,

$ a = -1 $
$ b = 6 $
$ c = -8 $

Since $ a < 0 $, the parabola opens downward, confirming a maximum value exists at the vertex.

Step 2: Calculate the x-Coordinate of the Vertex

The x-coordinate of the vertex is found using the formula:

🔗 Related Articles You Might Like:

📰 herscan 📰 florida special election 2025 📰 best travel backpacks 📰 New Evidence Crazy Car Game And It Sparks Outrage 📰 Event Manager App 📰 Https Www Crazygames Com 📰 Seeone Unlocked The Shocking Secrets Behind This Location You Thought You Knew 2309861 📰 Best Day To Buy Plane Tickets 748901 📰 Q By Peter Chang 2963330 📰 Power Platform Login 📰 Spiderman Female Villains 📰 From Heroes To Humanity The Son Who Redefined Son For Father Forever 7206310 📰 How To Clean Up Icloud Storage 1802976 📰 Top Cryptocurrency 📰 Police Confirm Wells Fargo Merchant Services Fees And It Changes Everything 📰 3 Top 10 Asmr Online Videos That Put You In A Trance Instantly 3391265 📰 Vampire Crawlers 📰 Xenojiiva 7574201

Final Thoughts

$$
x = -rac{b}{2a}
$$

Substitute $ a = -1 $ and $ b = 6 $:

$$
x = -rac{6}{2(-1)} = -rac{6}{-2} = 3
$$

So, the vertex occurs at $ x = 3 $.

Step 3: Substitute to Find the Maximum y-Value

Now plug $ x = 3 $ back into the original equation to find $ y $:

$$
y = -(3)^2 + 6(3) - 8 = -9 + 18 - 8 = 1
$$

Thus, the maximum height is $ y = 1 $ unit.