Graphs & Coordinates

    Cards (18)

    • Midpoint of a graph (x1+x22\frac{x_1+x_2}{2} , y1+y22\frac{y_1+y_2}{2})
    • Gradient is given by:
      m=m= yx\frac{\bigtriangleup y}{\bigtriangleup x}
    • If m1m_1 and m2m_2 are perpendicular then
      m1=m_1= 1m2-\frac{1}{m_2}
      and m1m2=m_1m_2= 1-1
    • Equation of a line:
      y  y1=y\ -\ y_1= m(xx1)m\left(x-x_1\right)
    • if b24acb^2-4ac > 0 then there are 2 roots
    • if b24acb^2-4ac = 0 then 1 (repeated) root
    • if b24acb^2-4ac < 0 then no real roots
    • The picture represents the graph
      y=y=kx\frac{-k}{x}
    • The picture represents the graph
      y=y=kx2\frac{k}{x^2}
    • The picture represents the graph
      y=y=kx2\frac{-k}{x^2}
    • Equation for a circle with centre (a, b) and radius r:
      (xa)2\left(x-a\right)^2 + (yb)2\left(y-b\right)^2 = r2r^2
    • Sine graph
    • Cosine graph
    • Transformation f(x+a)f\left(x+a\right) will do a shift of (   0a_{\ \ 0}^{-a} )
    • Transformation af(x)af\left(x\right) will stretch in the y direction by scale factor aa
    • Transformation f(x)-f\left(x\right) will flip/reflect in the x axis
    • Transformation f(x)f\left(-x\right) will flip/reflect in the y axis
    • Transformation |f(x)f\left(x\right)| will flip up anything below the x axis
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