Write the quadratic in standard form: (y=ax^2+bx+c)
Identify the vertex using (x=-frac{b}{2a})
Substitute that (x)-value into the function to find the vertex (y)-value
Plot the vertex
Find the axis of symmetry: (x=-frac{b}{2a})
Determine whether the parabola opens up if (a>0) or down if (a<0)
Plot the (y)-intercept by using (c)
Find additional points by choosing (x)-values on both sides of the axis of symmetry
Use symmetry to reflect points across the axis of symmetry
Draw a smooth parabola through the plotted points
Check the graph for consistency with the vertex, axis of symmetry, and opening direction