Question 216553
 A line is described by the equation y = 3. A parabola is given by the equation Y = x^2 –6x +c What value(s) of c would result in this system of equations having one solution? What value(s) of c would result in two solutions?
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The x value of the vertex is -b/2a = 3
To have one value, the y of the vertex must be +3 (tangent to the line y=3).
3 = 9 - 18 + c
c = 12 for one value.
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For any c<12 there will be 2 crossings of the line y = 3, --> 2 solutions.