To determine the line of symmetry for the given quadratic function [tex]\( f(x) = 88x^2 - 264x + 300 \)[/tex], we use the standard formula for the axis of symmetry of a quadratic function of the form [tex]\( ax^2 + bx + c \)[/tex]:
The axis of symmetry, [tex]\( x \)[/tex], is given by:
[tex]\[ x = \frac{-b}{2a} \][/tex]
In the given function [tex]\( f(x) = 88x^2 - 264x + 300 \)[/tex]:
- [tex]\( a = 88 \)[/tex]
- [tex]\( b = -264 \)[/tex]
Let's calculate the line of symmetry using these values:
[tex]\[ x = \frac{-(-264)}{2 \cdot 88} \][/tex]
[tex]\[ x = \frac{264}{176} \][/tex]
[tex]\[ x = \frac{264}{176} = 1.5 \][/tex]
Therefore, the correct answer is:
A. The trajectory of the airplane is symmetric about the line [tex]\( x = 1.5 \text{ km} \)[/tex].
