Find by algebraic means the point of intersection of two graphs with equations y=x^2-3x +7 and y= 5 - x^2.
Since it is a point of intersection.....the point will satisfy BOTH of the equations....and they are equal at this point...so set them equal to each other
x^2-3x+7 = 5 - x^2 and solve for 'x'
then use this value of 'x' (there MAY be TWO values of 'x' !...and there may be NONE !!) in one of the equations to compute 'y'
x^2 - 3x + 7 = 5 - x^2 add x^2 to both sides......subtract 5 from both sides
2x^2 - 3x + 2 = 0 (1)
The dicriminant is
(-3)^2 - 4(2)(2) =
9 - 16 =
Thus.....if the discriminant is negative, we have no real solutions to (1)....so.....there are no intersection points as shown by the graph here :