4.2 quadratic functions objective: solve quadratic equations. use the discriminant to describe the...

4.2 Quadratic Functions Objective: Solve quadratic equations. Use the discriminant to describe the roots of a quadratic equation.

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4.2Quadratic Functions

Objective:Solve quadratic equations.Use the discriminant to describe the roots of a

quadratic equation.

Solve x2 – 12x + 7 = 0 by completing the square.

x2 – 12x = -7

x2 – 12x + 36 = -7 + 36

(x – 6)2 = 29

x – 6 = ± 29

x = 6 ± 29

Page 3: 4.2 Quadratic Functions Objective: Solve quadratic equations. Use the discriminant to describe the roots of a quadratic equation

Quadratic Formula

acbbx

Discriminant

acb 42

• If “D” is positive perfect square• 2, real, rational solutions

• If “D” is positive non-perfect square• 2, real, irrational solutions

• If “D” is zero• 1, real, rational double root

• If “D” is negative• Imaginary conjugates

Page 5: 4.2 Quadratic Functions Objective: Solve quadratic equations. Use the discriminant to describe the roots of a quadratic equation

Page 6: 4.2 Quadratic Functions Objective: Solve quadratic equations. Use the discriminant to describe the roots of a quadratic equation

Assignment

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