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**Solving Quadratic Equation by Graphing**

Section 6.1 and 6.2

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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 real solutions 2 imaginary solutions (use quadratic formula or completing square to find) One solution Two solutions Either 2 rational or 2 irrational (may need to use quadratic formula or completing the square to find)

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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 (a + min, a – max) The roots or zeros are the x-intercepts. The vertex is the maximum or minimum point. All parabolas have an axis of symmetry. (x = -b/2a) Y-intercept = c (0, c)

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**Graphing Quadratic Equations**

One method of graphing uses a table with arbitrary x-values. Graph y = x2 - 4x Roots 0 and 4 , Vertex (2, -4) , Axis of Symmetry x = 2 , y-intercept (0, 0) 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 Y-intercept 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 equation into y1 and 0 in for y2 To find min/max – 2nd trace min or max (also known as the vertex) To find roots – 2nd trace intersect and find where it crosses the x-axis.

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