Mathematics General - Graphs

Straight Line Graphs Standard Form: \(y = mx + b\) Features of a Straight Line Graph X-intercept: substitute \(y=0\) Y-intercept: value of \(b\) Transformations of a Straight Line Graph Vertical Translation Up: increase \(b\) Vertical Translation Down: decrease \(b\) Increase steepness: increase \(m\) Decrease steepness: decrease \(m\) Reflect in y-axis: \(m \times -1\) Reflect in x-axis: \(y \times -1\) AND \(m \times -1\) Reflect in Main Diagonal \((y=x)\): switch y and x Horizontal Translation Left: increase \(b\) Horizontal Translation Right: decrease \(b\) Lines Parallel to the Axis Standard Form (parallel to x-axis): \(y=b\) Standard Form (Parallel to y-axis): \(x=a\) Transformations of Lines Parallel to the Axis Vertical translation up: Increase \(b\) Vertical Translation Down: Decrease \(b\) Horizontal Translation Left: Decrease \(a\) Horizontal Translation Right: Increase \(a\) Parabolas General Form: \(y=ax^2 + bx + c\) Features of a Parabola X-Intercepts (not always present): intersects of parabola and \(y=0\) Y-Intercept: intersects of parabola \(x=0\).