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].
