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Summary IEB AP Math:Quadratic equations
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  • AP Math
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This document describes: -How to use the quadratic formula -Cubic polynomials -Solving cubic graphs -Long division -K substitution -Quadratic equation roots methods (given roots)

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  • March 4, 2021
  • 8
  • 2020/2021
  • Summary

Subjects

  • math
  • ieb
  • matric
  • ap math
  • quadratic
  • equation
  • ap
  • notes
  • summary

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  • 12
  • AP Math
  • 200
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Quadratic Equation
Formulas:

−𝑏 ± √𝑏 2 − 4𝑎𝑐
𝑥=
2𝑎
∆ = 𝑏 2 − 4𝑎𝑐
𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 = 𝑑𝑖𝑣𝑖𝑠𝑜𝑟 × 𝑄𝑢𝑜𝑡𝑖𝑒𝑛𝑡 + 𝑟𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟


Cubic polynomials
These are expressions that have the following format and returns 3 x-ints:


𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 + 𝑑 = 𝑦


where:
a = shape of the graph
d= y-int(where x=0)




a<0 a>0




How to solve cubic graphs:
1)Sub integer values (-2,-1…..2, 3) into the equation

, 2)If the y value is 0, then that x value is a root


Example:
If y = 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 + 𝑑
When x=2, then y=0, thus x=2 is a root


To get an equation:
𝑥=2
𝑥−2 = 2−2
𝑥−2 = 0




Methods to solve cubic equations:
𝑓(𝑥) = 𝑥 3 − 7𝑥 − 6


Step 1: Sub in random integers from -5 to 5
When y = 0, then you have found a factor


f(0) = -6
f(-1) = 0


Therefore (𝑥 + 1) is a factor


Method 1: Inspection


Using the 𝑥 + 1, write the equation in this format:


(𝑓𝑎𝑐𝑡𝑜𝑟)(𝑎𝑥 2 + 𝑏𝑥 + 𝑐) = 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛


Therefore:

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