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The function [tex]f[/tex] approximately represents the trajectory of an airplane in an air show, where [tex]x[/tex] is the horizontal distance of the flight, in kilometers.
[tex]\[ f(x) = 88x^2 - 264x + 300 \][/tex]

What is the symmetry of the function?

A. The trajectory of the airplane is symmetric about the line [tex]x = 1.5 \, \text{km}[/tex].
B. The trajectory of the airplane is not symmetric.
C. The trajectory of the airplane is symmetric about the line [tex]x = 102 \, \text{km}[/tex].
D. The trajectory of the airplane is symmetric about the line [tex]x = 2 \, \text{km}[/tex].



Answer :

GinnyAnswer
To determine the line of symmetry for the quadratic function given by [tex]\( f(x) = 88x^2 - 264x + 300 \)[/tex], we use the general form of a quadratic function [tex]\( ax^2 + bx + c \)[/tex]. The line of symmetry of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] is found using the formula:

[tex]\[ x = -\frac{b}{2a} \][/tex]

Here, the coefficients are:
- [tex]\( a = 88 \)[/tex]
- [tex]\( b = -264 \)[/tex]
- [tex]\( c = 300 \)[/tex]

Plugging these values into our formula for the line of symmetry, we get:

[tex]\[ x = -\frac{-264}{2 \cdot 88} \][/tex]

Simplify the numerator and the denominator:

[tex]\[ x = \frac{264}{176} \][/tex]

Perform the division:

[tex]\[ x = 1.5 \][/tex]

Therefore, the trajectory of the airplane is symmetric about the line [tex]\( x = 1.5 \)[/tex] km.

The correct answer is:
A. The trajectory of the airplane is symmetric about the line [tex]\( x = 1.5 \)[/tex] km.

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