SOLUTION: A quadratic-quadratic system of equations can have no solution, infinite solutions and two other possibilities. Graph two different quadratic-quadratic systems of equations below t

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Question 1195067: A quadratic-quadratic system of equations can have no solution, infinite solutions and two other possibilities. Graph two different quadratic-quadratic systems of equations below to demonstrate these two other possibilities.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


2 solutions....

(1) One with positive leading coefficient, the other with negative
Example: y=x^2-1 and y=-x^2+1
graph:

graph%28200%2C200%2C-3%2C3%2C-3%2C3%2Cx%5E2-1%2C-x%5E2%2B1%29

(2) Same thing, but with different axes of symmetry
Example: y=x^2-1 and y=-x^2+2x
graph:

graph%28200%2C200%2C-3%2C3%2C-3%2C3%2Cx%5E2-1%2C-x%5E2%2B2x%29

(3) Two with different positive leading coefficients; vertices one above the other
Example: y=x^2 and y=(1/2)x^2+1
graph:

graph%28200%2C200%2C-3%2C3%2C-1%2C5%2Cx%5E2%2C%281%2F2%29x%5E2%2B1%29

or 1 solution....

(1) same vertex but opening different directions (single intersection at the common vertex)
Example: y=x^2 and y=-x^2
graph:
graph%28200%2C200%2C-3%2C3%2C-3%2C3%2Cx%5E2%2C-x%5E2%29

(2) single intersection not at either vertex
Example: y=x^2+2x and y=-x^2+2x
graph:
graph%28200%2C200%2C-3%2C3%2C-3%2C3%2Cx%5E2%2B2x%2C-x%5E2%2B2x%29