All quadratic functions have the same type of curved graphs with a line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c \) has a minimum turning point when \(a \textgreater 0 \) ...

Plotting a graph takes time. Often mathematicians just want to know the key features. These are: shape, location and some key points (such as where the graph crosses the axes or turning points).