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

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:

📰 Shocked Your Fiddlesticks Build Used These Hidden Upgrades? Click to Reveal! 📰 Master Fiddlesticks Build Like a Pro—These Tweaks Will Blow Your Competitors Away! 📰 Why This Fiddlesticks Build Is Taking Over Streamers’ Setups—Performance That’s Straight Out of a Fantasy! 📰 Psycho Pass 8833279 📰 Uncharted Treasures Revealed The Ultimate Map Of Oregon Coast Youve Never Seen Before 5927801 📰 How To Send Read Receipt In Outlook 8441020 📰 These Javadoc Comments Reveal Secrets No Developer Knowsclick To Discover 8307931 📰 Why These Shippuden Fillers Buggered The Series The Full Scoop Inside 9881245 📰 Why Every Womans Wardrobe Needs A Beautiful Silver Braceletshop Now 258185 📰 Hole In The Wall Flatiron 6285503 📰 Crew Cab Truck Revolution The Durable Machine That Never Disappoints 8707635 📰 Flight Attendant Criteria 8656656 📰 From Humble Beginnings To Icon Masashi Kishimotos Stunning Journey Youre Missing 1417909 📰 From Wheels To Weights 220 Pounds Isnt Just A Figureits A Miracle In Kilograms 5432097 📰 Shocked By Sunpass Toll This Explosive Tip Could Slash Your Commute Costs Forever 300773 📰 What Is Sell Put 6247005 📰 Sikh Religion 1802446 📰 3 This Lesser Known Genius Of War Heinz Guderians Genius Tactics Fbi Never Clicked On 5102447

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.