How can you find solutions to equations?
You can use graphs and value-tables.
You can also employ algebraic methods: modifying
an equation to obtain another equation with the
same solutions as the original (an equivalent
equation), but with an easier-to-read solution.
For example, the linear equation 3x+1=x+9 is equivalent to the
equation 2x=8, which has an easy-to-read solution.
This activity is about solving quadratic equations using
algebraic methods.
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Some of the tasks in this activity suggest ideas related to
finding the solutions of quadratic equations.
Other tasks present several problems that can be solved more easily
by constructing quadratic equations and solving
them.
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Prepare a report on solving quadratic equations
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Explain how to solve various quadratic equations.
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Give examples of equations and show how you solve them.
In your examples, display cases that are different both in the form of the equation and in the number
of solutions. Use the tasks and exercises in this activity
if you need ideas for various forms of quadratic equations.
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Show how you check and verify your results.
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Do you think that you have a general method
for solving any quadratic equation? If you
think you do, explain what it is. If not,
give examples of equations that you find
problematic.
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Compare methods of solving equations by
algebraic processes with methods of solving equations
using graphs or value tables.
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