We want to solve the given by graphing. Note that both of the system are .
Let's graph each of them, one at a time.
We can write the boundary curve for Inequality (I) by replacing the greater than
sign with an equals
sign. Then, we can identify
we can find the . To do so, we will need to think of
as a function of
Let's substitute the values of
in the formula for the
-coordinate of the vertex.
-coordinate of the vertex is
Now, let's find the
-coordinate by substituting
into the for the boundary line.
The vertex is
With this, we know that the of the is the
Next, let's find two more points on the curve, one on each side of the axis of symmetry.
The points and are on the parabola. Let's plot the points and connect them with a smooth curve.
Now that we have the boundary curve, we need to determine which region to shade. To do so, we will use
as a test point. If the point satisfies the inequality, we will shade the region that contains the point. If not, we will shade the opposite region.
Since the substitution produced a true statement, we will shade the region that contains the point Because we have a strict inequality, the boundary curve will be dashed.
Once again, we can write the boundary curve by replacing the greater than sign with an equals sign.
We can draw the second parabola following the same procedure as with the first.
|| Axis of Symmetry
|| Two Points
Any point on the plane can be used to determine the region we should shade. Because this inequality is strict, the curve will be dashed.
The solution set is the overlapping region.