G-12: MATH FORMULA'S

x = -b/2a

What is the VERTEX FORMULA in finding x ?

1. The equation is quadratic (ax^2+bx+c)

2. The problem asks for a maximum or minimum (e.g., highest point, lowest cost, shortest time, greatest area).

3. The quadratic represents a real-world situation where something increases and then decreases (like a ball being thrown).

4. The problem does not ask for exact roots or solutions but instead for the highest/lowest point.

What are the CLUES that tell you you are going to use the formula x = -b/2a ?

R = Price × Quantity

How do you solve for REVENUE ?

an = a1 + (n-1)d

Formula for the nth Term of the ARITHMETIC SEQUENCE:

Sn = n/2(a1 + an) or Sn = n/2[2a1 + (n-1)d]

Series formula for the sum of n terms in an ARITHMETIC SEQUENCE:

an = a1 x r^(n-1)

Formula for the nth Term of the GEOMETRIC SEQUENCE:

Sn = a(1-r^n)/(1-r)

Series formula for the sum of n terms in an ARITHMETIC SEQUENCE (finite):

Sn = a/(1-r)

Series formula for the sum of n terms in an ARITHMETIC SEQUENCE (infinite):

an = 1/[a1 + (n-1)d]

Formula for the nth Term of the HARMONIC SEQUENCE:

Sn = ln/d {[ 2a + (2n - 10)d] / (2a - d)}

Series formula for the sum of n terms in an HARMONIC SEQUENCE:

sin^2 x + cos^2 x = 1

1 + tan⁡^2 x = sec⁡^2 x

1+ cot⁡^2 x = csc⁡^2 x

The 3 MOST IMPORTANT Pythagorean Identities:

sin 2x = 2sinxcosx

cos 2x = cos²x - sin²x

tan 2x = 2tanx / 1 - tan²x

The DOUBLE-ANGLE Identities

sin(A + B) = sinAcosB + cosAsinB
cos(A+B) = cosAcosB - sinAsinB
tan(A+B) = (tanA + tanB) / 1 - tanAtanB

The Sum & Difference Identities