An air show is scheduled for an airport located on a coordinate system measured in miles. the air traffic controllers have closed the airspace, modeled by a quadratic equation, to non-air show traffic. the boundary of the closed airspace starts at the vertex at (10, 6) and passes through the point (12, 7). a commuter jet has filed a flight plan that takes it along a linear path from (–18, 14) to (16, –13). which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?
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Which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?

 The answer is: The system of equations number three:

 y=1/4(x-10)²+6  (i)
 y=(-27/34)x-5/17  (ii)

 The reason is shown below:

 -The boundary of the closed airspace: (10,6); (12,7)

 -Linear path of the commuter jet: (-18,14) to (16,-13)

 y=1/4(x-10)²+6  (i)
 y=(-27/34)x-5/17  (ii)

 The first equation represents the boundary of the closed airspace, because the points (10,6) and (12,7) are contained in the equation:

 -For (10,6), we have:

 (i) 1/4(10-10)²+6
 6=6 (The equation is satisfied)

 -For (12,7):

 7=1/4(12-10)²+6
 7=4/4+6
 7=1+6
 7=7 (The equation is satisfied)

 The equation (ii) represents the path of the commuter jet, because the points (-18,14) and (16,-13) are contained in the equation:

 -For(16,-13):

 -13=(-27/34)x16-5/7
 -13=-13 (The equation is satisfied)

 -For (-18,14):

 14=(-27/34)x(-18)-5/7
 14=14 (The equation is satisfied)

 Therefore, by resolving the system of equations, we know that the commuter jet’s flight path intersects the closed airspace.

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