SOLUTION: Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). y=X^2-4x Please assist me with this answer, and show me

Algebra ->  Graphs -> SOLUTION: Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). y=X^2-4x Please assist me with this answer, and show me       Log On


   

Question 127398: Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). y=X^2-4x
Please assist me with this answer, and show me the proper graph and table.
Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the axis of symmetry, use this formula:

x=-b%2F%282a%29

From the equation y=x%5E2-4x we can see that a=1 and b=-4

x=%28--4%29%2F%282%2A1%29 Plug in b=-4 and a=1


x=4%2F%282%2A1%29 Negate -4 to get 4


x=%284%29%2F2 Multiply 2 and 1 to get 2



x=2 Reduce


So the axis of symmetry is x=2


So the x-coordinate of the vertex is x=2. Lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate f%282%29

f%28x%29=x%5E2-4x Start with the given polynomial


f%282%29=%282%29%5E2-4%282%29 Plug in x=2


f%282%29=%284%29-4%282%29 Raise 2 to the second power to get 4


f%282%29=-4 Now combine like terms


So the vertex is (2,-4)


Since the x-coordinate is 2, this means the axis of symmetry is x=2

Now lets find 2 other points to the left of the vertex


Lets evaluate f%280%29

f%28x%29=x%5E2-4x Start with the given polynomial


f%280%29=%280%29%5E2-4%280%29 Plug in x=0


f%280%29=%280%29-4%280%29 Raise 0 to the second power to get 0


f%280%29=%280%29-0 Multiply 4 by 0 to get 0


f%280%29=0 Remove any zero terms


So our 1st point is (0,0)



----Now lets find another point----



Lets evaluate f%281%29

f%28x%29=x%5E2-4x Start with the given polynomial


f%281%29=%281%29%5E2-4%281%29 Plug in x=1


f%281%29=%281%29-4%281%29 Raise 1 to the second power to get 1


f%281%29=%281%29-4 Multiply 4 by 1 to get 4


f%281%29=-3 Now combine like terms


So our 2nd point is (1,-3)


Now remember, the parabola is symmetrical about the axis of symmetry (which is x=2)
This means the y-value for x=1 is equal to the y-value of x=3. So when x=3, y=-3.
Also, the y-value for x=0 is equal to the y-value of x=4. So when x=4, y=0.


Now lets make a table of the values we have calculated 



 xy


 00
 

 1-3
 

 2-4
 

 3-3
 

 40


Now plot the points


Now connect the points to graph y=+x%5E2-4x. Also, to draw the axis of symmetry, simply draw a vertical line through the vertex
Graph of y=+x%5E2-4x (red) and the axis of symmetry (blue)