Question

select the correct answer.
function ( f ) approximately represents the trajectory of an airplane in an air show, where ( x ) is the horizontal distance of the flight, in kilometers
( f(x) = 88x^2 - 264x + 300 )
what is the symmetry of the function?
a. the trajectory of the airplane is symmetric about the line ( x = 2 ) km.
b. the trajectory of the airplane is not symmetric.
c. the trajectory of the airplane is symmetric about the line ( x = 102 ) km.
d. the trajectory of the airplane is symmetric about the line ( x = 1.5 ) km.

Explanation:

Step1: Recall the axis of symmetry formula for a quadratic function.

For a quadratic function in the form \( f(x) = ax^2 + bx + c \), the axis of symmetry is given by the formula \( x = -\frac{b}{2a} \).

Step2: Identify the values of \( a \) and \( b \) from the given function.

In the function \( f(x) = 88x^2 - 264x + 300 \), we have \( a = 88 \) and \( b = -264 \).

Step3: Substitute the values of \( a \) and \( b \) into the axis of symmetry formula.

\[
x = -\frac{-264}{2 \times 88}
\]
Simplify the numerator and the denominator:
The numerator \( -(-264) = 264 \), and the denominator \( 2 \times 88 = 176 \).
So, \( x = \frac{264}{176} \).
Simplify the fraction \( \frac{264}{176} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 88.
\( 264 \div 88 = 3 \) and \( 176 \div 88 = 2 \), so \( \frac{264}{176} = \frac{3}{2} = 1.5 \).
So, the axis of symmetry is \( x = 1.5 \) km, which means the trajectory of the airplane is symmetric about the line \( x = 1.5 \) km.

Answer:

D. The trajectory of the airplane is symmetric about the line \( x = 1.5 \) km.