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Solving Quadratic Equation by Graphing
Section 6.1
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Quadratic Equation y = ax2 + bx + c ax2 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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Identifying Terms Example f(x)=5x2-7x+1 Quadratic term 5x2
Linear term x Constant term 1
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Identifying Terms Example f(x) = 4x2 - 3 Quadratic term 4x2
Linear term Constant term
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Identifying Terms Now you try this problem. f(x) = 5x2 - 2x + 3
quadratic term linear term constant term 5x2 -2x 3
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Quadratic Solutions The number of real solutions is at most two.
No solutions One solution Two 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) = x2 - 4 Solutions are -2 and 2.
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Identifying Solutions
Now you try this problem. f(x) = 2x - x2 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 = x2 - 4x Axis of Symmetry x = 2 Roots 0 and 4 , Vertex (2, -4) , x y 1 -3 2 -4 3 4
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Graphing Quadratic Equations
Try this problem y = x2 - 2x - 8. Roots Vertex Axis of Symmetry x y -2 -1 1 3 4
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Graphing Quadratic Equations
The graphing calculator is also a helpful tool for graphing quadratic equations. Enter the equation in y1 on your calculator.
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