A curve has the equation y=x^2+4x+4 and a line has the equation y=2x+3. Show the line and curve have only one point of intersection and find its coordinate..
First set the equations equal to each other: x^2+4x+4 = 2x+3.Rearrange for x in form ax^2+bx+c : x^2+2x+1=0Factorise: (x+1)^2=0. Repeated root, hence only one intersection. x=-1. Using y=2x+3, y=1. So coordinate: (-1,1). Check answers by substituting values back into both equations. Note, I have chosen equations that can be easily factorised at every step so a graphical explanation could be easily conveyed.
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