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**6.3 Solving Quadratic Equations by Factoring**

Write a quadratic equation with given roots

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**Roots or Zeros of the Quadratic Equation**

The Roots or Zeros of the Quadratic Equation are the points where the graph hits the x axis. The zeros of the functions are the input that make the equation equal zero. Roots are 4,-3

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**To solve a Quadratic Equation**

Make one side zero. Then factor then set each factor to zero

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Solve

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Solve

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Solve

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Solve

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Solve

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Solve

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Solve Multiply the ends together and find what adds to the coefficient of the middle term

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Solve Use -6 and 1 to break up the middle term

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Solve Use group factoring to factor, first two terms and then the last two terms

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Solve

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**How to write a quadratic equation with roots**

Given r1,r2 the equation is (x - r1)(x - r2)=0 Then foil the factors, x2 - (r1 + r2)x+(r1· r2)=0

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**How to write a quadratic equation with roots**

Given r1,r2 the equation is (x - r1)(x - r2)=0 Then foil the factors, x2 - (r1 + r2)x+(r1· r2)=0 Roots are -2, 5 Equation x2 - (-2+5)x+(-2)(5)=0 x2 - 3x -10 = 0

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**How to write a quadratic equation with roots**

Roots are ¼, 8 Equation x2 -(¼+8)x+(¼)(8)=0 x2 -(33/4)x + 2 = 0 Must get rid of the fraction, multiply by the common dominator. 4 4x2 - 33x + 8 = 0

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Homework Page 304 # 15 – 41 odd

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Homework Page 304 # 14 – 42 even

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