Graphs & Coordinates

• Midpoint of a graph ($\frac{x_1+x_2}{2}$ , $\frac{y_1+y_2}{2}$)
• Gradient is given by:

  $m=$ $\frac{\bigtriangleup y}{\bigtriangleup x}$
• If $m_1$ and $m_2$ are perpendicular then

  $m_1=$ $-\frac{1}{m_2}$

  and $m_1m_2=$ $-1$
• Equation of a line:

  $y\ -\ y_1=$ $m\left(x-x_1\right)$
• if $b^2-4ac$ > 0 then there are 2 roots
• if $b^2-4ac$ = 0 then 1 (repeated) root
• if $b^2-4ac$ < 0 then no real roots
• The picture represents the graph

  $y=$$\frac{-k}{x}$

  
• The picture represents the graph

  $y=$$\frac{k}{x^2}$

  
• The picture represents the graph

  $y=$$\frac{-k}{x^2}$

  
• Equation for a circle with centre (a, b) and radius r:

  $\left(x-a\right)^2$ + $\left(y-b\right)^2$ = $r^2$
• Sine graph

  
• Cosine graph

  
• Transformation $f\left(x+a\right)$ will do a shift of ( $_{\ \ 0}^{-a}$ )
• Transformation $af\left(x\right)$ will stretch in the y direction by scale factor $a$
• Transformation $-f\left(x\right)$ will flip/reflect in the x axis
• Transformation $f\left(-x\right)$ will flip/reflect in the y axis
• Transformation |$f\left(x\right)$| will flip up anything below the x axis