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Solving Quadratic Equations

Presentation of Solving Quadratic Equations by graphing, factoring, and quadratic formula

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Solving Quadratic Equations

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  1. Solving Quadratic Equations Objective: Students will solve quadratic equations by graphing, factoring, and quadratic formula.

  2. Solving Quadratic Equations by Graphing Steps: 1. Write the equation as a function. Replace the zero with y. 2. Graph the function. a. Find the axis of symmetry. b. Use the axis of symmetry to find the vertex. c. Determine the y-intercept. d. Find an additional point. e. Graph the points and reflect them across the axis of symmetry. f. Connect the points with a smooth curve called a parabola. 3. Find the zeros of the function. *The zeros of a function are the solutions. The zeros are where the parabola crosses the X-axis.

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  5. PRACTICE

  6. Solving Quadratic Equations by Factoring When solving a quadratic equation, you factor the same as you would factor a polynomial expression. *Without a Leading Coefficient When the equation is in standard form, find two factors of your "c" that add to give you your "b". *With a Leading Coefficient When the equation is in standard form, Multiply your "a" and "c". Determine two factors of the product that add to give you "b". Rewrite the expression using the factors. Factor by grouping.

  7. To find the solutions, you need to use the zero product property. *The zero product property: If the product of two quantities equals zero, at least one of the quantities equals zero. ** Think about it: If you multiply two numbers and get zero for your answer, one of them must be zero. Once you have factored the quadratic expression, set each polynomial equal to zero and solve. This will give you your solutions.

  8. EXAMPLE

  9. EXAMPLE

  10. PRACTICE

  11. Solving Quadratc Equation using the Quadratic Formula Steps: 1. Make sure the equation is in standard form. 2. Identify your "a", "b", and "c". 3. Plug your "a", "b", and "c" into the formula. 4. Simplify by using the order of operations. (Start with what is under the radical)

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