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Solving Quadratic Equations Tammy Wallace Varina High

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What is a Quadratic Equation? A QUADRATIC EQUATION is an equation in which the greatest power of any variable is 2. The standard form of a quadratic equation is, where a, b, and c are real numbers and a ≠ 0.

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Quadratic Equations The factors of a quadratic equation in standard from are related to the x-intercepts of the graph of its related function. Therefore, you can find or confirm the factors of a polynomial by looking at the x-intercepts of the graph of its related function.

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___ _ Use the graphing calculator to plot at least 4 points. Where are the x- intercepts located? (0, -5) and (0, 2) What is the relation between the factored form and the x- intercepts? The factors, when solved for zero, give the location of the x- intercepts.

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+ 2 +2 - 5 -5

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Solving Quadratic Equations Both methods, factoring and graphing, can be used to solve quadratic equations. There several ways we can describe the solutions to quadratics. The following words may be used when asked to find the solution to a quadratic equation: 1.X-intercepts 2.Solutions 3.Roots 4.Zeros

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Where are the x- intercepts located? (0, -4) and (0, 1) The solution is {-4, 1}

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Where are the x- intercepts located? (0, 5) and (0, 7) What are the solutions? {5, 7}

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{-5, -3}

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Given the solution, {-4, 2}, what is the quadratic equation.

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Given the graph, what is the quadratic equation.

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Where else can roots be found? Roots, solutions, x-intercepts or zeros can also be found for linear equations. To find the solution of a linear equation, set the equation equal to zero and solve for x. The answer also can be solved or verified by graphing as well.

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The solution is {2}

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