Question

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

Determine the symmetry of the function.

A. The trajectory of the airplane is symmetric about the line x = 102 km, which indicates that the height of the airplane when it moves a horizontal distance of 101 km is the same as the height of the airplane when it moves a horizontal distance of 103 km.

B. The trajectory of the airplane is not symmetric.

C. The trajectory of the airplane is symmetric about the line x = 1.5 km, which indicates that the height of the airplane when it moves a horizontal distance of 0.5 km is the same as the height of the airplane when it moves a horizontal distance of 2.5 km.

D. The trajectory of the airplane is symmetric about the line x = 2 km, which indicates that the height of the airplane when it moves a horizontal distance of 1 km is the same as the height of the airplane when it moves a horizontal distance of 3 km.

Answer 1

Answer:

The trajectory of the airplane is symmetric about the line x = 1.5 km.

Step-by-step explanation:

PLATO test

Answer 2

Answer:

C. is your answer

Step-by-step explanation:

In order to determine the line of symmetry, it would help to put this standard form parabola into vertex form, which is

$y=a(x-h)^2+k$,

where x = h is the equation of the line of symmetry.

To get this into vertex form we will complete the square.  The first couple of steps I will combine into 1.  We will set the quadratic equal to zero, then move the constant over to the other side:

$88x^2-264x=-300$

The next rule is that the leading coefficient HAS to be a positive 1.  Ours is a positive 88, so we have to factor it out:

$88(x^2-3x)=300$

Now we can perform the process of completing the square.  The rule is to take half the linear term, square it, and add it to both sides.  Our linear term is 3.  Half of 3 is 3/2, and 3/2 squared is 9/2.  We will add 9/2 inside the parenthesis on the left, but don't forget about that 88 sitting out front which refuses to be ignored.  It serves as a multiplier into the parenthesis.  What we actually added in, then, was 88(9/2) which is 198:

$88(x^2-3x+\frac{9}{4})=-300+198$

The purpose of completing the square is to give us a perfect square binomial which serves as the axis of symmetry of the parabola and also gives us the h coordinate of the vertex.  We will state that binomial and at the same time do the addition on the right:

$88(x-\frac{3}{2})^2=-102$

Now we can move the constant back over and set it back equal to y:

$y=88(x-\frac{3}{2})^2+102$

From that form you can see that the equation of the line of symmetry is x = 1.5.  The coordinates of the vertex are (1.5, 102).  If we move 1 unit to the left of the vertex, or 1 unit to the right of the vertex, we will be at the same height.

C then is your answer.