Home » 國際課程 » IB課程 » Details

IB DP Maths: AI SL復習筆記2.2.3 Properties of Graphs

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月19日上午11:11

- If?a?is positive?then the vertex is the?minimum?point
- If?a?is negative?then the vertex is the?maximum?point

2.2.1-Quadratic-Graphs-Notes-Diagram-1

Use your GDC to find the roots and the turning point of a quadratic function
- You do not need to factorise or complete the square
- It is good exam technique to sketch the graph from your GDC as part of your working

2-2-3-ib-ai-sl-quad--cub-graphs-a-we-solution

2-2-3-ib-ai-sl-quad--cub-graphs-b-we-solution

These can be found using your GDC

- These are also called the?x-intercepts
- There can be 1, 2 or 3?x-intercepts
  - There is always at least 1
There are either?0 or 2 local minimums/maximums
- If there are 0 then the curve is?monotonic?(always increasing or always decreasing)
- If there are 2 then one is a local minimum and one is a local maximum

2.7.1-Sketching-Polynomials-Notes-Diagram-1

2-2-3-ib-ai-sl-quad--cub-graphs-c-we-solution

The coefficient of?x?and the constant?k?determine whether the graph is?increasing or decreasing
- If the coefficient of?x?and?k?have the?same sign?then?graph is increasing
- If the coefficient of?x?and?k?have?different signs?then the?graph is decreasing
There is at?most 1 root
- It can be found using your GDC

2-2-3-ib-ai-sl-exp-graphs-a-we-solution

2-2-3-ib-ai-sl-exp-graphs-b-we-solution

The?maximum value?is?y?=?a?+?d
The?minimum value?is?y?= -a?+?d
The?principal axis?is the horizontal line halfway between the maximum and minimum values
- This is?y?=?d
The?amplitude?is the vertical distance from the principal axis to the maximum value
- This is?a