Write the quadratic in standard form: y = ax^2 + bx + c
Identify a, b, and c
Find the vertex using x = -b / (2a)
Substitute the x-value into the function to find the y-value of the vertex
Plot the vertex
Find the axis of symmetry: x = -b / (2a)
Find the y-intercept by setting x = 0
Plot the y-intercept
Find additional points by choosing x-values on both sides of the vertex
Use symmetry to plot matching points
Determine whether the parabola opens up or down from the sign of a
Draw a smooth curve through the plotted points
Check that the graph is symmetric about the axis of symmetry