SOLUTION: I need help with this please: The military is performing missile tests. A new missile is launched from the ground and it's path can be modelled by the quadratic equation y=-4(x-

Algebra ->  Graphs -> SOLUTION: I need help with this please: The military is performing missile tests. A new missile is launched from the ground and it's path can be modelled by the quadratic equation y=-4(x-      Log On


   

Question 1195069: I need help with this please:
The military is performing missile tests. A new missile is launched from the ground and it's path can be modelled by the quadratic equation y=-4(x-10)^2+400, where y is the missile's height in meters and x is the time in seconds. 10 seconds later, a second heat-seeking missile is launched to intercept and explode the first missile before it reaches the ground. The second missile's path can be modelled by the quadratic equation y=2(x-20)^2+300, where y is its height in meters and x is its time in seconds. At what time and height should the second missile reach and explode the first missile.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
y=-4(x-10)^2+400
y=2(x-20)^2+300 -> should be y=+-2%28x-20%29%5E2%2B300
solve the system
y=-4%28x-10%29%5E2%2B400
y=+-2%28x-20%29%5E2%2B300
The first and second missile will intersect at x that makes
-2%28x-20%29%5E2%2B300=-4%28x-10%29%5E2%2B400
-2x%5E2+%2B+80x+-500=80x+-+4+x%5E2..........divide by+2
-x%5E2+%2B+40x+-250=40x+-+2+x%5E2
2+x%5E2-x%5E2+%2B+40x+-250-40x+=0
x%5E2++-250+=0
x%5E2++=250+
x+=sqrt%28250+%29
x+=15.81
y=-4%2815.81-10%29%5E2%2B400=264.98
the point of intersection is (15.81,264.98)
so, after 15.81 seconds the second missile will reach and explode the first missile at height of +264.98m