Solving equations
Quadratic equations of the type
[vertex form]=[constant]
One of the simplest quadratic equations is of the type:
2x² = 18.
By performing translations of one or both of its sides, you can obtain many new equations. For example:
The left side of this equation is a correspondence rule of a quadratic
function in vertex form;
the right side is a constant function.
Examine these equations and develop
general methods for finding their solutions.
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Exercise 2, Exercise 3, and Exercise 4
provide special examples of equations of the type [vertex form]=[constant].
Exercise 5
provides general examples of equations of the type [vertex form]=[constant].
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Develop a general method for solving equations of the type
[vertex form]=[constant]
Examine the examples generated by
the exercises linked above and discuss the following
questions regarding equations of the type
[vertex form]=[constant]:
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When are there no solutions to the equation?
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When is there one solution?
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When is there more than one solution?
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How can you find these solutions?
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