# advanced graphs and using them

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- Created by: Japtha Woodward
- Created on: 16-06-13 10:52

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- Maths
- Advanced graphs
- Solving quadratic and linear equations simultaneously
- the point where 2 graphs meet is the simultaneous solution for both equations
- 1. eliminate by substituting quadratic equation into linear equation.
- 2. rearrange to = 0
- 3. factorise then solve
- Substitute value of x back into linear equation to find y coordinates

- Intersection of a circle and a line
- Equation of a circle
- Can be found using Pythagoras theorem: x2+y2=r2
- Form x2+y2 = r

- Coordinates must satisfy both equations
- 1. rewrite linear equation in form y=
- 2. Eliminate by substituting into circle equation
- 3. expand brackets, rearrange and factorise
- 4. substitute x value into linear equation to find y

- Equation of a circle
- Functions and transformations
- y=f(x)
- f= any function that occurs to x

- Finding graphs of related functions can be found applying transformations
- y=f(x)+a moves up or down on x-axis by value of a
- y=f(x+a) moves graph a units to left/ right.
- if it is +a, move graph to left
- if it is -a, move graph to right

- y=a x f(x) stretches graph along y-axis
- All x values stay same, but y values are multiplied by a

- y=f(ax)
- If a>1, graph stretches inwards by 1/a
- e.g. if y=(2x)2 the x coordinates are x 1/2

- Untitled

- If a>1, graph stretches inwards by 1/a

- y=f(x)

- Solving quadratic and linear equations simultaneously

- Advanced graphs

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