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Solving Quadratic Equations by Graphing

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Quadratic Equation y = ax 2 + bx + c ax 2 is the quadratic term. bx is the linear term. c is the constant term. The highest exponent is two; therefore, the degree is two.

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Quadratic Solutions The number of real solutions is at most two. No solutionsOne solutionTwo solutions

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Solving Equations When we talk about solving these equations, we want to find the value of x when y = 0. These values, where the graph crosses the x-axis, are called the x-intercepts. These values are also referred to as solutions, zeros, or roots.

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Identifying Solutions Example f(x) = x 2 - 4 Solutions are -2 and 2.

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Identifying Solutions Now you try this problem. f(x) = 2x - x 2 Solutions are 0 and 2.

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Graphing Quadratic Equations The graph of a quadratic equation is a parabola. The roots or zeros are the x-intercepts. The vertex is the maximum or minimum point. All parabolas have an axis of symmetry.

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Graphing Quadratic Equations One method of graphing uses a table with arbitrary x-values. Graph y = x 2 - 4x Roots 0 and 4, Vertex (2, -4), Axis of Symmetry x = 2 xy 00 1-3 2-4 3-3 40

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