Is the plane in danger? Why or why not?

Question

A missle is lauched along a path determined by the equation f(x)=-2x^2+72x, where f(x) is the height of the missle in feet x seconds after the launch. A plane is flying nearby at a height of 650 feet.

Answer 1

Typically an equation like this is given in the form

 

h(t) = -2t^2 + 72t, so that you remember that t is the time and h is the height of the missile at time t.

 

If you replace h(t) with 650, and solve for t, you can find out at what time the missile will be 650 feet high.

 

So, you get

 

650 = -2t^2 + 72t

 

or 2t^2 - 72t +625 = 0

 

factor out the 2, and use the quadratic to solve for t.  You will find a negative number under the radical,

 

which implies the missile will never be 650 feet high at a positive time t.  So the plane is safe.