SOLUTION: if the graph of the function f(x)=4x^2-20x-4 intersects the graph of the function g(x)=1+4x-x^2 at the point (m,k), show that the other point of intersection occurs where x= -1/m.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: if the graph of the function f(x)=4x^2-20x-4 intersects the graph of the function g(x)=1+4x-x^2 at the point (m,k), show that the other point of intersection occurs where x= -1/m.      Log On


   

Question 156381: if the graph of the function f(x)=4x^2-20x-4 intersects the graph of the function g(x)=1+4x-x^2 at the point (m,k), show that the other point of intersection occurs where x= -1/m.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
if the graph of the function f%28x%29=4x%5E2-20x-4 intersects the graph of the
function g%28x%29=1%2B4x-x%5E2 at the point (m,k), show that the other point of
intersection occurs where x=+-1%2Fm.
f%28x%29=4x%5E2-20x-4
g%28x%29=1%2B4x-x%5E2

To find their points of intersection, set 

f%28x%29=g%28x%29
4x%5E2-20x-4=1%2B4x-x%5E2
5x%5E2-24x-5=0

%28x-5%29%285x%2B1%29=0

x-5=0   5x%2B1=0
  x=5     5x=-1
           x=-1%2F5

So if m=5, then -1%2Fm+=+-1%2F5 and that is the 
other value of x where the graphs intersect.

Edwin