Add linear quadratic functions to
one side of the equation to obtain new equations with
the following properties:
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An equation with two solutions, one of which is 4 (as in the original equation), and the other will change.
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An equation with two solutions, one of which is -8 (as in the original equation), and the other will change.
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An equation with two solutions: -8 and 8.
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An equation with solutions identical to those of the original equation.
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An equation with only one solution: 4.
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An equation that has no solutions.
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In each case, explain whether you can achieve the desired
change
- by adding a linear function to one of the sides,
- by adding a quadratic function to one of the sides,
or in both ways. If you think it cannot be accomplished in one
of these ways, explain why.
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