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Graphing Quadratic Equations

This comprehensive guide covers the essential concepts of quadratic equations in general and standard form, including the equation y = ax² + bx + c. Learn effective factoring techniques using the greatest common factor (GCF) and the Square Root Method. Discover how to handle missing linear terms and apply Perfect Square Trinomials. Additionally, explore the Difference of Squares and solve equations by completing the square. We’ll also investigate real-world applications like maximizing sales for a product through quadratic modeling.

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Graphing Quadratic Equations

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  1. Graphing Quadratic Equations

  2. General Form of a Quadratic Equation y = ax2 + bx + c

  3. Standard Form ax2 + bx + c = 0

  4. Factoring and Solving • Rule 1 (the only rule) • Find the G.C.F. • Otherwise, look for something familiar

  5. If factoring does not seem to be working….. • Ask the following question: • “Is the linear term missing?” • If so, SQUARE ROOTS SEEM GOOD.

  6. Square Root Method • If you take the square root of both sides of an equation, then you must get TWO answers. Don't forget the

  7. PERFECT SQUARED TRINOMIALS • “FIRST TERM SQUARED PLUS TWICE THE FIRST TIMES THE LAST PLUS THE LAST TERM SQUARED.” • Can be factored from a memorized formula.

  8. Differences of Squares • A difference of two squares can be factored. • Remember that the inner and outer terms must be opposites.

  9. A manufacturer determines that the number of drills it can sell is given by the formula where p is the price of the drills in dollars. • At what price will the manufacturer sell the • maximum number of drills? • b. What is the maximum number of drills that can be sold?

  10. Factor the expression.

  11. or Solve by factoring.

  12. Solve the equation by finding square roots

  13. Solve the equation.

  14. Solve the equation.

  15. Solve by completing the square.

  16. Solve by completing the square.

  17. Rewrite in Vertex Form

  18. Rewrite in Vertex Form

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