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.
