10-4 Quadratic Equations - Solve with Quadratic Formula

10-4 Quadratic Equations - Solve with Quadratic Formula.notebook March 10, 2016

1

Ex 1:

10-4 Quadratic Equations - Solve with Quadratic Formula

How many answers will I have?

( - 5)( - 6) = 0

x =

x2 + 10x + 25 = 0

Two answers.

(x + 5)(x + 5) = 0

x = -5 , -5or

x = -5

One answer.

x2 = -9x2 = -9

You cannot take square root of a negative.

No Solution.orTWO imaginary solutions.

Discriminant: used to find the number of solutions for a quadratic equation.

ax2 + bx + c = 0b2 - 4ac

If discriminant is positive, there are 2 solutions.

If discriminant is zero, there is only 1 solution.

If discriminant is negative, there is no solution or 2 imaginary solutions.

Step2:

Step1: Place in a-b-c form. Move all terms left & make equation = 0.

- 5- 5

-6x2 - 4x - 2 = 0

-6x2 - 4x - 2 = 0

a b c

a = -6 b =c = -2

Step3: b2 - 4acb2 - 4ac

(-4)2 - 4(-6)(-2)

16 - 4(12)

16 - 48

Discriminant = -32

ANSWER


10-4 Quadratic Equations - Solve with Quadratic FormulaChecks for Example 1

b - 4ac

b - 4ac

b - 4ac

ANSWERANSWER

ANSWER ANSWER

ANSWERANSWER

10-4 Quadratic Equations - Solve with Quadratic Formula.notebook April 14, 2016

10-4 Quadratic Equations - Solve with Quadratic FormulaWhy completing the square is not

2 2 2 2

x - 3x - 1 = 0 2 2

Easiest way to solve is to useQuadratic Formula:

Discriminant

2 2 2 2

10-4 Quadratic Equations - Solve with Quadratic Formula.notebook April 14, 2016

a b c

+


x = (-3) (-3) - 4(2)(-1) 2(2)

Ex 2:Solve using the quadratic formula.

Step1: Identify , & c

a = 2 b = -3 c = -1

Step2: Plug , & c. into quadratic formula.

x = +3 9 - 4(-2)4

x = 3 9 -84

x = 3 9 +84

ANSWER

or

DiscriminantHow many answers?

a b c

x = 3 4


10-4 Quadratic Equations - Solve with Quadratic FormulaChecks for Example 2



-continuedChecks for Example 2Solve each equation with the quadratic formula.

inside a radical.

No Solution.



2 4 22 4 2

2(1 2 2 )

2( )2 4 22 2

2 4x2( )2 4x2 2

2(1 2x)ANSWER

ANSWER

10-4 Quadratic Equations - Solve with Quadratic Formula.notebook June 07, 2021

x = -2 4 74

x = -2 74

x = -2 28

x = -2 4 +24

4


Ex 3:

Step2: Identify , & c.

Step1: Place in a-b-c form. Move all terms left & make equation = 0.

Step3: Plug , & c. into quadratic formula.

Solve using the quadratic formula.

2x2 + 2x - 3 = 0

a b c

2x + 2x - 3 = 0a = 2b = 2c =

x = 2) (2 2 - 4(2 -3)

2(2)

x = -2 4 - 4(-6

4

4Simply Radical

-x2 + 2x - 3 = -3x2

-x + 2x - 3 = -3x

a b c

2x

x = -2 4 - -244

10-4 Quadratic Equations - Solve with Quadratic Formula.notebook June 07, 2021


Ex 3:

ANSWER

-continued



Checks for Example 3:



Checks for Example 3:10

-continuedSolve each equation with the quadratic formula.



Checks for Example 3:11

-continued

Solve each equation with the quadratic formula.

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10-4 Quadratic Equations - Solve with Quadratic Formula