Essential Steps - Sketching Quadratic Graphs in Vertex Form

Sketching of graphs of quadratic functions given in the form of

\(y=\pm {{\left( x-p \right)}^{2}}+q,\,\,\,\,p>0,q>0\)

Step 1:

State the coefficient of \({{x}^{2}}\) to determine if the graph opens upwards or downwards.

Step 2:

Since the equation is of the form \(y=\pm {{\left( x-p \right)}^{2}}+q\), the coordinates of the minimum/maximum point are \(\left( p,q \right)\).

Step 3:

Obtain the \(y\)-intercept by substituting \(x=0\) into the equation.

Step 4:

Obtain the \(x\)-intercepts by substituting \(y=0\) into the equation.

Step 5:

Sketch the graph.