To address the symmetry of the quadratic function [tex]\( f(x) = 88x^2 - 264x + 300 \)[/tex]:
1. Identify the coefficients:
The given quadratic function is in the form [tex]\( ax^2 + bx + c \)[/tex]. Here:
- [tex]\( a = 88 \)[/tex]
- [tex]\( b = -264 \)[/tex]
- [tex]\( c = 300 \)[/tex]
2. Recall the formula for the axis of symmetry:
For any quadratic function [tex]\( ax^2 + bx + c \)[/tex], the axis of symmetry, which is the vertical line that passes through the vertex of the parabola, is given by:
[tex]\[
x = -\frac{b}{2a}
\][/tex]
3. Substitute the coefficients into the formula:
[tex]\[
x = -\frac{-264}{2 \times 88}
\][/tex]
4. Calculate the value:
[tex]\[
x = \frac{264}{176} = 1.5
\][/tex]
Thus, the symmetry of the trajectory of the airplane, which is represented by the function [tex]\( f(x) = 88x^2 - 264x + 300 \)[/tex], is about the line [tex]\( x = 1.5 \)[/tex].
So, the correct answer is:
A. The trajectory of the airplane is symmetric about the line [tex]\( x = 1.5 \)[/tex] km.
