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 linear 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?

Question

phi · Answer

I think they want you to find the equations for the line and for the parabola

You can find the equation of line by finding the slope between the two points
and then using
y - y0 = m (x - x0)
where (x0, y0) is a point on the line (you can use either of the 2 that are given)
and m is the slope

the parabola has an equation
y - yv = k (x - xv)^2  where (xv, yv) is the vertex.
(They do not say if the parabola is vertical or horizontal... complain to your teacher about this, but I assume they mean a vertical parabola $ \cup $ shaped

to find k, you the point (5,4) in the above equation.