What is the axis of symmetry of [tex]h(x)=-2 x^2+12 x-37[/tex]?
A. [tex]x=-15[/tex]
B. [tex]x=-3[/tex]
C. [tex]x=3[/tex]
D. [tex]x=15[/tex]

Identify the coefficients a and b from the quadratic function h ( x ) = − 2 x 2 + 12 x − 37 .
Apply the formula for the axis of symmetry: x = − 2 a b ​ .
Substitute the values a = − 2 and b = 12 into the formula: x = − 2 ( − 2 ) 12 ​ .
Simplify the expression to find the axis of symmetry: x = 3 ​ .

Explanation

Understanding the Problem We are given the quadratic function h ( x ) = − 2 x 2 + 12 x − 37 . Our goal is to find the axis of symmetry of this function. The axis of symmetry for a quadratic function in the standard form f ( x ) = a x 2 + b x + c is given by the vertical line x = − 2 a b ​ .

Identifying Coefficients In our given function, h ( x ) = − 2 x 2 + 12 x − 37 , we can identify the coefficients as follows:


a = − 2 b = 12 c = − 37

Applying the Formula Now, we will use the formula for the axis of symmetry, which is x = − 2 a b ​ . Substituting the values of a and b into the formula, we get:

x = − 2 ( − 2 ) 12 ​

Simplifying the Expression Simplifying the expression, we have:

x = − − 4 12 ​ x = 3

Final Answer Therefore, the axis of symmetry of the given quadratic function is x = 3 .

Examples
The axis of symmetry is a crucial concept in understanding quadratic functions. For example, consider a parabolic bridge arch described by a quadratic function. The axis of symmetry would represent the central line of the arch, helping engineers determine the bridge's structural balance and load distribution. Knowing the axis of symmetry allows for efficient design and analysis, ensuring the bridge's stability and symmetry.

Answered by GinnyAnswer | 2025-07-08

The axis of symmetry of the quadratic function h ( x ) = − 2 x 2 + 12 x − 37 is x = 3 .
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Answered by Anonymous | 2025-07-15