SOLUTION: Can someone explain to me step by step the following a lot of my classmates and including myself do not understand these problems. For problem # 22 Directions: Complete the

Algebra ->  Graphs -> SOLUTION: Can someone explain to me step by step the following a lot of my classmates and including myself do not understand these problems. For problem # 22 Directions: Complete the       Log On


   

Question 77590: Can someone explain to me step by step the following a lot of my classmates and including myself do not understand these problems.

For problem # 22
Directions: Complete the table, and describe the resulting graphs by identifying the vertex point, the graph’s direction, and any axis intercepts gleaned from the table or graph.
y = 2x^2

Problem #24
Directions: Complete the table, and describe the resulting graphs by identifying the vertex point, the graph’s direction, and any axis intercepts gleaned from the table or graph.
Y= x + 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#22
Table of y=2x%5E2 


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%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+2x%5E2%29+ graph of y=2x%5E2
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
0=2x%5E2
x%5E2=0 Divide both sides by 2
sqrt%28x%5E2%29=sqrt%280%29 Take the square root of both sides
x=0 So this is our root and it confirms what both the graph and the table show.









#24
Table of y=x%2B1 


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%28+300%2C+200%2C+-3%2C+2%2C+-5%2C+5%2C+x%2B1%29+ graph of y=x%2B1
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:
0=x%2B1
0-1=x%2Bcross%281-1%29 Subtract 1 from both sides
x=-1 So this is our root and it confirms what both the graph and the table show.