Math

• What is CTS?

  Complete the square
• What is the CTS formula?

  1. 1/2 the linear coefficient (b)
  2. Square that
  3. Add it on
• What is a trick you can do when you see: x^4 +3x^2 + 4

  Add on 1x^2 - 1x^2 (a.k.a adding nothing!)
• After you "add nothing" to a 3 term equation, what's the next step?

  Diamond box, then factor the cows.
• What number set is used in the Domain and Range?

  Real numbers
• How do you compare the "child" to the "parent"?

  • if a>0 it opens up
  • if a<0 it opens down
  • if |a|>1 it's skinnier than the parent
  • if |a|<1 it's wider than the parent
• What is the slope for F(x) = 0.1x^2 on [1,4] (1 ≤ x ≤ 4)

  slope(m) = F(4)-F(1) / 4-1

  = 0.5
• What are two ways to find the vertex?

  1. ( -b / 2(a) , b^2 - 4(a)(c) / -4(a) )
  2. y = a(x-h)^2 + k
• What is the vertex of y = 1(x-2)^2 + 3?

  V = ( 2 , 3 )
• (x+2)^2 = x^2 + 8x + 16
• (x-2)^2 = x^2 - 8x + 16
• (x+2)(x-2) = x^2 - 4x
• Perimeter = L(x) + W(x) -> L = W + P

  Area = L x W
• How do you find the area?


  A(x) = (2w + 2x)(w +x)

  (replace the length with the width)
• After you set up the area, what's next?

  Box!
• Formula for gravity?


  f(x) = -16T^2 + VoT + ho
• • Vo = initial velocity
  • ho = initial height
  • T = time
• Velocity function -> Vertex -> at h sec, k ft high
• How do you find the max height?


  Remove "c" off of Velocity Form (mainly vertex form).
• How could you find, how long something was in the air?

  1. Velocity form without "ho"
  2. Vertex form
  3. Divide feet by 5280, to convert to miles
• How do you maximize an area?

  1. Find the factored perimeter
  2. Put perimeter into Area form
  3. Area form into Vertex form
  4. V = ( w , max ft )
  5. Put w (from step 4.) into perimeter
  6. W by L, max ft^2
• How can you find the current income?

  1. Price-hikes = 0
  2. Rental charge: $rental price + 0(increase)
  3. Rental lose: item - 0(rental)
  4. Multiply: step 2. x step 3.
• How can you maximize your income?


  1. Make the price-hike equal "x".
  2. Box it
  3. Vertex form
  4. Then add/subtract the "h" (from step 3.) from the rental price.

  Find max income from replacing it... blah blah blah.