# Blog Post – Week 6

### * Developing and Applying the Quadratic Formula

• The solution of a quadratic equation, a𝑥² + b𝑥 + c = 0, where a,b, and c constants a ≠ 0, is given by the quadratic formula:  𝑥=  -b ±√b² – 4ac  ∕  2a

#### Examples

1. 3𝑥² + 6𝑥 – 4 = 0

a = 3, b = 6, b = -4

𝑥 = -6 ±√6² – 4(3)(-4) / 2(3)

𝑥 = -6 ±√36 + 48 / 6

𝑥 = -6 ±√84 / 6

𝑥 = -1 ±√14

# Solving Radical Equations – Week 5 blog post

2. Square both sides of the equation: If  x = y then x² = y²
3. Once the radical is removed, solve for the unknown

Example.

1. 𝒙² – 3 =13

+3        +3

√𝒙² = √16

𝒙 = 4

𝒙 = 4

2.  √𝒙+8 = 3

(√𝒙+8)² = 3²

𝒙 + 8 = 9

𝒙 = 1

# Week 4 blog post

•     When adding and subtracting radical the startegies for simplyfying polynomials can be used to symplify sums and differences of radicals. Like terms or like radicals in a sum or difference of radicals have the same radicand and the same index

Example

1. 7√9 – 4√9 = 3√9
• 7√9 and 4√9 are like terms becasue they have the same radicand and the same index. combine like terms.

2. ∛384 – ∛162 + ∛750

= 4∛6 – 3∛6 + 5∛6

= ∛6 + 5∛6

= 6∛6

• The radicands are different , so simplyify each radical, then solve it

# Week 3 blog post – Absolute Value of a Real Number

This week I learned about absolute value of a real number. Every real number can be represented as a point on a number line. The sign of the number indicates its position relative to 0. The magnitude of the number indicates its distance from 0.

The absolute value of -6 is  |-6|=6

Example:

|6-4| (7+9) – 6 (4-6)

= |2| (16) – 6 (-2)

= 2(16) – (-12)

= 32 +12

= 44

# Week 2 – Infinite geometric series

Infinite geometric series

S∞= a/1-r                    a=7,  r=0.2 or 1/5        3, 3/5, 3/25, 3/125…..

S∞=7/1-1/5

S∞=7÷4/5

S∞=35/4

This week , I learn Infinite Geometric Series. An infinite geometric series has an infinite number of terms. To determine the sum of an infinite geometric series, we need to know a, a is the t1. Common ratio is -1 < r < 1 . The sum of the series, S∞ is : S∞=a/1-r

# Week 1 – My Arthmetic Sequence

Arithmetic sequence – 3, 7, 11, 15, 19……

Formula – tn= t1+(n-1)d

t50=?

d=4

n=50

tn= t1+(n-1)d

t50=3+(50-1)4

t50=3+(49 x 4)     (49×4=196)

t50=3+196

t50=199

Sum of 50

Formula – Sn = n/2 (t1 + tn)

S50 = 50/2 (t1 + t50)

S50 = 25 (3 + 199)

S50 = 25 x 202

S50 = 5050