10
QuizMultiple Choice

Modeling with Systems — Quiz

Question 10 • Advanced Algebra: Concepts and Connections

A radio tower is located on a coordinate system measured in miles. The range of a signal in a particular direction is modeled by a quadratic function where the boundary of the signal starts at the vertex at open paren 4 comma 2 close paren It passes through the point open paren 5 comma 4 close paren A linear road connects points open paren negative 3 comma 7 close paren and open paren 8 comma 2 close paren Which system of equations can be used to determine whether the road intersects the boundary of the tower’s signal?

Answer
A
y minus open paren x minus 4 close paren squared is equal to 2 11 x plus 5 y is equal to 2
B
y minus 2 times open paren x minus 4 close paren squared is equal to 2 5 x plus 11 y is equal to 62
C
y minus 2 times open paren x minus 4 close paren squared is equal to 2 11 x plus 5 y is equal to 2
D
y minus open paren x minus 4 close paren squared is equal to 2 5 x plus 11 y is equal to 62

Explanation

A quadratic with vertex (4, 2) has the form y = a(x − 4)² + 2. Using the point (5, 4) gives 4 = a(5 − 4)² + 2, so a = 2 and the quadratic is y − 2(x − 4)² = 2. The road’s slope through (−3, 7) and (8, 2) is −5/11, which gives the line 5x + 11y = 62. These equations are in choice B.

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