Method One: Graph x2 + 2x - 8 ≤ y [or y ≥ x2 + 2x - 8]
Graph y = x2 + 2x - 8

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


Find the vertex, x-intercepts and y-intercept

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


Table of values

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


Use a solid line as the original inequality isn't strict (y ≥ x2 - 4x + 3)

Two Variable Equality Graph

Graph y ≥ x2 + 2x - 8

Choose a "test" location that is not part of the graph of the equality y = x2 - 4x + 3. 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 + 2x - 8               Substitute ( 0, 0 ) into the quadratic inequality

(0) ≥ (0)2 + 2(0) - 8       Simplify

0 ≥-8                             (TRUE)


Two Variable Inequality Graph

Graph 0 ≥ x2 + 2x - 8 [x2 + 2x - 8 ≤ 0]

View only the x-axis portion of the graph.

Video does not play in this browser or device. Please try another device or upgrade your browser.