THE COMPOUND // FIELD NOTES // WEEK 27
Parabolas, markups, and function arithmetic
Field Book
Lessons 100 to 103
Due
Test 24 due ยท Supplement 27
Method
Paper first, every step
The x squared family reports for graphing. Shift it, flip it, stretch it, and label the vertex before anything else.
What you have to be able to do
- Graph parabolas from the x squared parent
- Compute markups and selling prices
- Add and multiply functions, and run long division on polynomials
The procedures
Graphing parabolasField Book Lesson 100
- Start from y = x2. Adding inside shifts left, subtracting shifts right, adding outside lifts.
- A negative out front flips it over. Mark the vertex first, then two symmetric points.
Percent markupField Book Lesson 101
- Markup is a percent of the purchase price added to the purchase price.
- Selling price = purchase price times (1 + rate).
Function arithmeticField Book Lesson 102
- (f + g)(x) = f(x) + g(x), and products work the same way.
- Evaluate each piece separately, then combine.
Polynomial long divisionField Book Lesson 103
- Leave a column for every power, writing zero terms as placeholders.
- Divide, multiply, subtract, bring down: same rhythm as arithmetic.
Worked: a 30 percent markup
- A shop buys at 40 and marks up 30 percent.
- Selling price = 40(1 + 0.30) = 40 times 1.3.
- The tag reads 52.
Terms on the record
| Term | Meaning |
|---|
| parabola | the graph of the x squared family |
| vertex | the turning point of a parabola |
| markup | a percent of the purchase price added on to set the selling price |