advanced graphs and using them

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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
      • 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
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