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Solving Basic One-Variable Quadratic Equations

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Lesson Plans and Worksheets for Algebra I
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Common Core For Algebra I

Examples, solutions, and videos to help Algebra I students learn how to use appropriate and efficient strategies to find solutions to basic quadratic equations.
Students interpret the verbal description of a problem and its solutions in context and then justify the solutions using algebraic reasoning.

New York State Common Core Math Algebra I, Module 4, Lesson 6

Worksheets for Algebra 1

Lesson 6 Summary

By looking at the structure of a quadratic equation (missing linear terms, perfect squares, factored expressions) you can find clues for the best method to solve it. Some strategies include setting the equation equal to zero, factoring out the GCF or common factors, and using the zero product property.

Be aware of the domain and range for a function presented in context and consider whether or not answers make sense in that context.

Lesson 6 Examples

Solving quadratic equations (some with missing the linear variable)
3x2 - 27 = 0
(x - 3)2 = 1
x2 - 5x + 7 = 1
2(x - 3)2 = 12

Lesson 6 Problem Set Sample Solutions


5. 4(g - 1)2 + 6 = 13

7. Mischief is a toy poodle who competes with her trainer in the agility course. Within the course, Mischief must leap through a hoop. Mischief’s jump can be modeled by the equation h = - 16t2 + 12t , where h is the height of the leap in feet and is the time since the leap, in seconds. At what values of does Mischief start and end the jump?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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