AIR MATH

Math Question

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 \( (4,2) \). It passes through the point \( (5,4) \). A linea road connects points \( (-3,7) \) and \( (8,2) \). Which system of equations can be used to determine whether the road intersects the boundary of the tower's signal? \( \left\{\begin{array}{r}y-2(x-4)^{2}=2 \\ 5 x+11 y=62\end{array}\right. \) \( \left\{\begin{array}{r}y-(x-4)^{2}=2 \\ 5 x+11 y=62\end{array}\right. \) \( \left\{\begin{array}{r}y-(x-4)^{2}=2 \\ 11 x+5 y=2\end{array}\right. \) \( \left\{\begin{array}{r}y-2(x-4)^{2}=2 \\ 11 x+5 y=2\end{array}\right. \)

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