6.3 Solving Quadratic Equations by Factoring

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

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

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

Solve

Solve

Solve

Solve

Solve

Solve

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

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

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

Solve

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

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

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

Homework Page 304 # 15 – 41 odd

Homework Page 304 # 14 – 42 even