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The function [tex]\( f(x) = 88x^2 - 264x + 300 \)[/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.

What is the symmetry of the function?

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



Answer :

GinnyAnswer
To determine the symmetry of the quadratic function [tex]\( f(x) = 88x^2 - 264x + 300 \)[/tex], we need to find the axis of symmetry of the parabola.

A quadratic function of the form [tex]\( ax^2 + bx + c \)[/tex] has its axis of symmetry at the line [tex]\( x = -\frac{b}{2a} \)[/tex].

For the given function:
[tex]\[ a = 88 \][/tex]
[tex]\[ b = -264 \][/tex]

We use the formula for the axis of symmetry:
[tex]\[ x = -\frac{b}{2a} \][/tex]

Substituting the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[ x = -\frac{-264}{2 \cdot 88} \][/tex]
[tex]\[ x = \frac{264}{176} \][/tex]
[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]\( x = 1.5 km \)[/tex].

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