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Solving Quadratic Equation by Graphing Section 6.1

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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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Example f(x)=5x 2 -7x+1 Quadratic term 5x 2 Linear term -7x Constant term 1 Identifying Terms

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Example f(x) = 4x 2 - 3 Quadratic term 4x 2 Linear term 0 Constant term -3 Identifying Terms

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Now you try this problem. f(x) = 5x 2 - 2x + 3 quadratic term linear term constant term Identifying Terms 5x 2 -2x 3

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The number of real solutions is at most two. Quadratic Solutions 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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Example f(x) = x 2 - 4 Identifying Solutions Solutions are -2 and 2.

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

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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. Graphing Quadratic Equations

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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 Graphing Quadratic Equations xy 00 1-3 2-4 3-3 40

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Try this problem y = x 2 - 2x - 8. Roots Vertex Axis of Symmetry Graphing Quadratic Equations xy -2 1 3 4

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The graphing calculator is also a helpful tool for graphing quadratic equations. Refer to classwork1 for directions for graphing quadratic equations on the Casio. Graphing Quadratic Equations

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