A curve has an equation of `y=x^2-4+4` and a line has equation y=mx+c, where m is constant. For the case where m=1, the curve and the line intersect at the points A and B. Find the coordinates of the midpoint of AB.
We are asked to find the midpoint of the segment joining the intersection points of the curve `y=x^2-4x+4` and the line `y=x+c` (we are told that m is a constant and m=1—we let c vary.) **If you really meant `y=x^2-4+4` (which means`y=x^2`) the following steps would still apply.**
A line and a parabola (the graph of a quadratic function) will either not intersect at all, intersect at exactly one point (the line is tangent to the curve), or at at most two points which we will label A and B. Let the midpoint be M.
To find the intersection of two curves we set the equations equal...
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