10-4 quadratic equations - solve with quadratic formula
TRANSCRIPT
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 Formula.notebook March 10, 2016
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
+
10-4 Quadratic Equations - Solve with Quadratic Formula
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 Formula.notebook March 10, 2016
10-4 Quadratic Equations - Solve with Quadratic FormulaChecks for Example 2
10-4 Quadratic Equations - Solve with Quadratic Formula.notebook March 10, 2016
610-4 Quadratic Equations - Solve with Quadratic Formula
-continuedChecks for Example 2Solve each equation with the quadratic formula.
inside a radical.
No Solution.
10-4 Quadratic Equations - Solve with Quadratic Formula.notebook March 10, 2016
710-4 Quadratic Equations - Solve with Quadratic Formula
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
810-4 Quadratic Equations - Solve with Quadratic Formula
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
910-4 Quadratic Equations - Solve with Quadratic Formula
Ex 3:
ANSWER
-continued
10-4 Quadratic Equations - Solve with Quadratic Formula.notebook March 10, 2016
910-4 Quadratic Equations - Solve with Quadratic Formula
Checks for Example 3:
10-4 Quadratic Equations - Solve with Quadratic Formula.notebook March 10, 2016
10-4 Quadratic Equations - Solve with Quadratic Formula
Checks for Example 3:10
-continuedSolve each equation with the quadratic formula.
10-4 Quadratic Equations - Solve with Quadratic Formula.notebook March 10, 2016
10-4 Quadratic Equations - Solve with Quadratic Formula
Checks for Example 3:11
-continued
Solve each equation with the quadratic formula.