THE COMPOUND // FIELD NOTES // WEEK 19
Calculator week and the quadratic formula
Field Book
Lessons 68 to 71
Due
Test 16 due · Supplement 18
Method
Paper first, every step
Lesson 68 is the calculator lesson: no new notes, everyone drills powers and roots on their own machine until it obeys. Then the quadratic formula arrives, built from completing the square.
What you have to be able to do
- Compute powers and roots correctly on your calculator
- Keep isolating the variable before evaluating in gas problems
- Apply the quadratic formula
The procedures
Calculator disciplineField Book Lesson 68
- Practice scientific notation entry, powers, and roots until the keystrokes are automatic.
- The machine follows order of operations only if you give it the parentheses.
Gas problemsField Book Lesson 69
- Isolate the unknown variable first, then substitute the numbers.
- Carry the units through and confirm they cancel.
Distribute firstField Book Lesson 70
- In advanced abstract equations, distribute before collecting terms.
- Then clear fractions, collect the target, factor, divide.
The quadratic formulaField Book Lesson 71
- Start from ax2 + bx + c = 0 and complete the square in general: the result is the formula.
- x = -b ± √(b2 - 4ac)2a. Memorize it as a sentence.
Worked: the formula on a known case
- Solve x2 + 4x + 3 = 0 with the formula.
- x = -4 ± √(16 - 12)2 = -4 ± 22.
- x = -1 or x = -3, matching the factored answer.
Terms on the record
| Term | Meaning |
|---|
| standard form | a quadratic arranged as ax2 + bx + c = 0 |
| quadratic formula | the general solution built by completing the square on standard form |
| radicand of the formula | b2 - 4ac, the quantity under the formula's root |