Find the vertex, x-intercepts and y-intercept, then make a small table of values.

Create a table of values using the x-value of the vertex as a "middle" value.

Plot the locations in the table of values then draw the resulting graph.

Use a dotted line as the original inequality is strict (y < x² - 4x + 1)

Choose a "test" location that is not part of the graph of the equality y = x² - 4x + 1. If the origin is not part of the graph of the equality, it is a "good" location to choose. Substitute the values associated with the test location into the inequality.

y < x² - 4x + 1               Substitute ( 0, 0 ) into the quadratic inequality

(0) < (0)² - 4(0) + 1       Simplify

0 < 1                             (TRUE)

View only the x-axis portion of the graph.