Question

A lighthouse is located at (1, 2) in a coordinate system measured in miles. A sailboat starts at (–7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). Which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse?

Answer 1

you need an equation for the distance from quadratic function to point (1,2)
\[d = \sqrt{(x-1)^2 + (y-2)^2}\]
\[y = (x-2)^2 - 6\]
then set up the inequality to see if its less than 5 miles
\[\sqrt{(x-1)^2 +((x-2)^2 - 8)^2} \le 5\]