swbat… use the quadratic formula to solve quadratic equations fri, 5/10 agenda 1. wu (15 min) 2....
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SWBAT… use the Quadratic Formula to solve quadratic equations Fri, 5/10
Agenda 1. WU (15 min)2. Quadratic Formula (30 min)
Warm-Up:
Given y = x2 + 5x + 61. Find the domain and range2. Find the solutions
HW#5: Study Guide
The Quadratic Formula
a
acbbx
2
42
YOU MUST MEMORIZE THIS FORMULA!!!
What Does The Formula Do?
The Quadratic formula allows you to find the roots of a quadratic equation (if they exist) even if the quadratic equation does not factorise.
The formula states that for a quadratic equation of the form :
ax2 + bx + c = 0
The roots of the quadratic equation are given by :
a
acbbx
2
42
Example 1
Use the quadratic formula to solve the equation x2 + 5x + 6 = 0
Solution:
x2 + 5x + 6 = 0
a = 1 b = 5 c = 6
a
acbbx
2
42
)1)(2(
)6)(1)(4(55 2 x
2
)24(255 x
2
15 x
2
15
2
15
xorx
x = -2 or x = -3
These are the roots of the equation.
Example 2
Use the quadratic formula to solve the equation 8x2 + 2x – 3= 0
Solution:
8x2 + 2x – 3 = 0
a = 8 b = 2 c = -3
a
acbbx
2
42
)8)(2(
)3)(8)(4(22 2 x
16
)96(42 x
16
1002 x
16
102
16
102
xorx
x = ½ or x = -¾
These are the roots of the equation.
Example 3
Use the quadratic formula to solve the equation 8x2 – 22x + 15 = 0
Solution:
8x2 – 22x + 15 = 0
a = 8 b = -22 c = 15
a
acbbx
2
42
)8)(2(
)15)(8)(4()22()22( 2 x
16
)480(484(22 x
16
422 x
16
222
16
222
xorx
x = 3/2 or x = 5/4
These are the roots of the equation.
a = -2 b = 5 c = 3
a
acbbx
2
42
)2)(2(
)3)(2)(4(55 2
x
4
24255
x
4
15
4
15
xorx
x = ½ or x = -3/4
What is wrong with this student’s work? What are the correct solutions?
Use the quadratic formula to solve the equation -2x2 + 5x + 3= 0
a = -2 b = 5 c = 3
a
acbbx
2
42
)2)(2(
)3)(2)(4(55 2
x
4
)24(255
x
4
75
4
75
xorx
x = -2/4 = -1/2 or x = 3
Use the quadratic formula to solve the equation -2x2 + 5x + 3= 0
4
495
x
Example 4
The Discriminant
In the Quadratic Formula, the expression under the radical sign, b2 – 4ac is called the discriminant.
The discriminat can be used to determine the number of real solutions of a quadratic equation.
Key Concept: Using the DiscriminantEquation Example
Discriminant
Graph of Related
Function
Number of Real
Solutions
Key Concept: Using the DiscriminantEquation Example
x2 + 2x + 5 = 0 x2 + 10x + 25 = 0 2x2 – 7x + 2 = 0
Discriminant
Graph of Related
Function
Number of Real
Solutions
Key Concept: Using the DiscriminantEquation Example
x2 + 2x + 5 = 0 x2 + 10x + 25 = 0 2x2 – 7x + 2 = 0
Discriminant Negative Zero Positive
Graph of Related
Function
Number of Real
Solutions
Key Concept: Using the DiscriminantEquation Example
x2 + 2x + 5 = 0 x2 + 10x + 25 = 0 2x2 – 7x + 2 = 0
Discriminant Negative Zero Positive
Graph of Related
Function
0 x-intercepts 1 x-intercepts 2 x-intercepts
Number of Real
Solutions
Key Concept: Using the DiscriminantEquation Example
x2 + 2x + 5 = 0 x2 + 10x + 25 = 0 2x2 – 7x + 2 = 0
Discriminant Negative Zero Positive
Graph of Related
Function
0 x-intercepts 1 x-intercepts 2 x-intercepts
Number of Real
Solutions0 1 2
SWBAT… use the Quadratic Formula to solve quadratic eqns. Tues, 5/24
Agenda 1. WU (10 min)2. Review HW#5 (10 min)3. HW#6 – Study Guide
WARM-UP Given the function f(x) = 3x2 – 18x + 15, for
what values of x does f(x) = 0.
HW#6: Quadratics Study Guide