The curve y=x^2-3x-4 crosses the x-axis at P and Q. The tangents to the curve at P and Q meet at R. The normals to the curve at P and Q meet at S. Find the distance RS.

Question

phi · Answer

I would find P and Q and sketch the graph just to get a feel for what is going on.
can you find P and Q ?  (factor the quadratic)

anonymous · Answer

(x-4)(x+1)

phi · Answer

yes.  at the x-axis y=0
so we have
(x-4)(x+1)=0
this means either x=4  or x=-1

this is a parabola,  with a vertex at -b/2a  with b= -3 and a=1
so it has a min at 3/2   

y = (3/2)^2- 3*3/2 -4 = -6.25

Can you sketch out the problem?

phi · Answer

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