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6.3 Solving Quadratic Equations by Factoring Write a quadratic equation with given roots.

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Presentation on theme: "6.3 Solving Quadratic Equations by Factoring Write a quadratic equation with given roots."— Presentation transcript:

1 6.3 Solving Quadratic Equations by Factoring Write a quadratic equation with given roots

2 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

3 To solve a Quadratic Equation Make one side zero. Then factor then set each factor to zero

4 Solve

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

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

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

13 Solve

14 How to write a quadratic equation with roots Given r 1,r 2 the equation is (x - r 1 )(x - r 2 )=0 Then foil the factors, x 2 - (r 1 + r 2 )x+(r 1 · r 2 )=0

15 How to write a quadratic equation with roots Given r 1,r 2 the equation is (x - r 1 )(x - r 2 )=0 Then foil the factors, x 2 - (r 1 + r 2 )x+(r 1 · r 2 )=0 Roots are -2, 5 Equationx 2 - (-2+5)x+(-2)(5)=0 x 2 - 3x -10 = 0

16 How to write a quadratic equation with roots Roots are ¼, 8 Equationx 2 -(¼+8)x+(¼)(8)=0 x 2 -(33/4)x + 2 = 0 Must get rid of the fraction, multiply by the common dominator. 4 4x x + 8 = 0

17 Homework Page 304 #15 – 41 odd

18 Homework Page 304 #14 – 42 even


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