Answered

Is it possible for a system of two quadratic equations to have exactly three solutions?
(Hint: Rotations of the graphs of quadratic equations still represent quadratic equations.)
O Yes, it is possible if both quadratic equations open up or open down.
Yes, it is possible if one of the quadratic equations is rotated 90° and opens to the right
or to the left.
No, it is not possible. Graphs of two quadratic functions cannot intersect at more than
two points.
No, it is not possible. Graphs of two quadratic functions can intersect at more than two
points, but not at exactly three points.



Answer :

GinnyAnswer
It is not possible for a system of two quadratic equations to have exactly three solutions. Here's why: 1. When you graph quadratic equations, they form parabolas. These parabolas can intersect at most two points. This is a fundamental property of quadratic functions. 2. Even if you rotate or shift the graphs of the quadratic equations, they will still maintain their basic shape as parabolas and intersect at most two points. Rotations or translations do not change the fact that a quadratic equation can have at most two solutions. 3. Therefore, the statement that a system of two quadratic equations can have exactly three solutions is incorrect based on the nature of quadratic functions and their graphical representation.

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