Modeling with Polynomial Functions: Polynomial Functions — Test
Question 10 • Advanced Algebra: Concepts and Connections
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 open paren 10 comma 6 close paren and passes through the point open paren 12 comma 7 close paren A commuter jet has filed a flight plan that takes it along a linear path from open paren negative 18 comma 14 close paren to open paren 16 comma negative 13 close paren Which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?
Answer
A
y is equal to 1 fourth times open paren x minus 10 close paren squared plus 6 y is equal to negative 2 x minus 22
B
y is equal to 1 fourth times open paren x minus 5 close paren squared plus 10 y is equal to negative 1 half x plus 5
C
y is equal to 1 fourth times open paren x minus 5 close paren squared plus 10 y is equal to negative 2 x minus 22
D
y is equal to 1 fourth times open paren x minus 10 close paren squared plus 6 y is equal to negative 27 over 34 x minus 5 over 17
Explanation
A parabola with vertex (10, 6) has the form y = a(x − 10)² + 6. Since it passes through (12, 7), 7 = 4a + 6, so a = 1/4. The jet’s path has slope (−13 − 14)/(16 − (−18)) = −27/34; substituting (−18, 14) gives a y-intercept of −5/17. Thus the system is y = 1/4(x − 10)² + 6 and y = −27/34x − 5/17, which is choice B.
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