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Simplifying Quadratic Equations: Techniques and Practice

This section covers techniques for recognizing and simplifying various quadratic equations. Learn how to identify equations reducible to quadratic forms, including those with even powers, radical equations, fractional exponents, and binomial terms. It introduces a simple method to solve quadratic equations by substituting a placeholder variable, solving, and then back-substituting to find the original variable. Includes practice problems for even powers, radicals, fractional exponents, negative exponents, and binomials to reinforce concepts, along with an introduction to graphs of quadratics.

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Simplifying Quadratic Equations: Techniques and Practice

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  1. Transformers – Simplifying the Complex 8.5

  2. Section 8.5 Equations Reducible to Quadratic Forms • Recognizing Equations that are Quadratic Form • Even Powers 4, 6, 8 and Up • Radical Equations – square roots, fourth roots, etc • Fractional Exponents ½, ¼, and Down • Binomial Terms 8.5

  3. SolvingQuadratic Form EquationsAlways 3 Terms: ax2n + bxn + c = 0 • If the 1st term’s variable part equals the square of the 2nd term’s variable part, you can use the following quadratic form technique: • Use a placeholder variable(u usually) to replace the 1st and 2nd term variables, solve as a quadratic, then back-substitute u with the variable and solve again. 8.5

  4. Practice – Even Powers 8.5

  5. Practice - Radicals 8.5

  6. Practice – Fractional Exponents 8.5

  7. Practice – Negative Exponents 8.5

  8. Practice - Binomials 8.5

  9. What Next? Graphs of Quadratics • Present Section 8.6 8.5

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