Summary
Summary IEB AP Math:Quadratic equations
This document describes: -How to use the quadratic formula -Cubic polynomials -Solving cubic graphs -Long division -K substitution -Quadratic equation roots methods (given roots)
[Show more]
Content preview
Quadratic EquationFormulas:
−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:
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller lucianIrsigler64. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R50,00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
66579 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now