#22
Table of
x | y
--------
-2 | 8
-1 | 1
0 | 0
1 | 1
2 | 8
Notice that the y values start at a high number and decrease. Then after x=0, they start to increase again. This shows us the vertex (the highest or lowest point) is (0,0) which we can see by this graph:
graph of
From this graph we can see the direction changes from a negative slope to a positive slope, and the graph is opening in the positive direction. Also we can see the x-intercepts are (0,0). We can solve for the x intercepts by letting y=0
Divide both sides by 2
Take the square root of both sides
So this is our root and it confirms what both the graph and the table show.
#24
Table of
x | y
--------
-2 | -1
-1 | 0
0 | 1
1 | 2
2 | 3
Notice that the y values increase as x increases. This means there is no vertex (there is no highest or lowest point). We can see this from the graph
graph of
From this graph we can see the graph has a positive slope, so it's going in the positive direction. Also we can see the x-intercept is (-1,0). We can solve for the x-intercept by letting y=0:
Subtract 1 from both sides
So this is our root and it confirms what both the graph and the table show.