Shade accordingly. If the test point satisfied the inequality, we shade the region that contains the point. If the test point did not satisfy the inequality, we shade the opposite region.
Step 1
Let's draw the graph of the related quadratic function, which is y=- 4x^2+12x-7. First we will use a table of values to find points on the function.
x
y=- 4x^2+12x-7
Simplify
(x,y)
x= 0
y=- 4( 0)^2+12( 0)-7
y= -7
( 0, -7)
x= 1
y=- 4( 1)^2+12( 1)-7
y= 1
( 1, 1)
x= 1.5
y=- 4( 1.5)^2+12( 1.5)-7
y= 2
( 1.5, 2)
x= 2
y=- 4( 2)^2+12( 2)-7
y= 1
( 2, 1)
x= 2.5
y=- 4( 2.5)^2+12( 2.5)-7
y= -2
( 2.5, -2)
Now we can use these points to draw the function.
Step 2
Next, let's determine which region to shade by testing a point. For simplicity, we will use (0,0) as our test point. Let's see if it satisfies the given inequality.
Since (0,0) produced a true statement, we will shade the region that contains the point. Also, note that the inequality is not strict. Therefore, the parabola will be solid.
