# advanced graphs and using them

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• Created by: bio1423
• Created on: 16-06-13 10:52
• Maths
• 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
• 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