Question

Maximum value of $-x^2 + 6x - 8$ is

• A. 3
• B. 2
• C. 1
• D. 0

Answer 1

Answer:

C. 1

To find the maximum value of the quadratic expression $-x^2 + 6x - 8$, we can find the vertex of the parabola.

Since the coefficient of $x^2$ is negative ($-1$), the parabola opens downwards, meaning its vertex represents the maximum value.

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Step 1: Identify the coefficients
From the expression $-x^2 + 6x - 8$:

• $a = -1$

• $b = 6$

• $c = -8$

Step 2: Find the x-coordinate of the vertex
The formula for the x-coordinate where the maximum occurs is:
$x = \frac{-b}{2a}$

Substitute the values:
$x = \frac{-6}{2(-1)} = \frac{-6}{-2} = 3$

Step 3: Substitute $x = 3$ back into the expression to find the maximum value
$\text{Maximum Value} = -(3)^2 + 6(3) - 8$
$\text{Maximum Value} = -9 + 18 - 8$
$\text{Maximum Value} = 9 - 8 = \mathbf{1}$

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Final Answer

The maximum value of the expression is 1.