Identify the quadratic function in standard form: (y=ax^2+bx+c)
Find the vertex using (x=-frac{b}{2a})
Substitute the x-value into the function to find the y-value of the vertex
Plot the vertex on the coordinate plane
Determine the axis of symmetry: (x=-frac{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 axis of symmetry
Use symmetry to find matching points
Plot all points
Draw a smooth parabola through the points
Check whether the parabola opens upward if (a>0)
Check whether the parabola opens downward if (a<0)
Verify the graph is symmetric about the axis of symmetry