SOLUTION: Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). Could someone help me please? {{{y=x^2-5x+4}}}

Algebra ->  Graphs -> SOLUTION: Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). Could someone help me please? {{{y=x^2-5x+4}}}      Log On


   

Question 102742: Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). Could someone help me please?
y=x%5E2-5x%2B4
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%5E2-5x%2B4 we can see that a=1 and b=-5

x=%28--5%29%2F%282%2A1%29 Plug in b=-5 and a=1


x=5%2F%282%2A1%29 Negate -5 to get 5


x=%285%29%2F2 Multiply 2 and 1 to get 2


So the axis of symmetry is x=5%2F2


So the x-coordinate of the vertex is x=5%2F2 (which is x=2.5 in decimal form). Lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate f%282.5%29

f%28x%29=x%5E2-5x%2B4 Start with the given polynomial


f%282.5%29=%282.5%29%5E2-5%282.5%29%2B4 Plug in x=2.5


f%282.5%29=%286.25%29-5%282.5%29%2B4 Raise 2.5 to the second power to get 6.25


f%282.5%29=%286.25%29-12.5%2B4 Multiply 5 by 2.5 to get 12.5


f%282.5%29=-2.25 Now combine like terms


So the vertex is (2.5,-2.25)


Since the x-coordinate is 2.5, this means the axis of symmetry is x=2.5

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


Lets evaluate f%280%29

f%28x%29=x%5E2-5x%2B4 Start with the given polynomial


f%280%29=%280%29%5E2-5%280%29%2B4 Plug in x=0


f%280%29=%280%29-5%280%29%2B4 Raise 0 to the second power to get 0


f%280%29=%280%29-0%2B4 Multiply 5 by 0 to get 0


f%280%29=4 Remove any zero terms


So our 1st point is (0,4)



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



Lets evaluate f%281%29

f%28x%29=x%5E2-5x%2B4 Start with the given polynomial


f%281%29=%281%29%5E2-5%281%29%2B4 Plug in x=1


f%281%29=%281%29-5%281%29%2B4 Raise 1 to the second power to get 1


f%281%29=%281%29-5%2B4 Multiply 5 by 1 to get 5


f%281%29=0 Now combine like terms


So our 2nd point is (1,0)


Now remember, the parabola is symmetrical about the axis of symmetry (which is x=2.5)
This means the y-value for x=1 is equal to the y-value of x=4. So when x=4, y=0.
Also, the y-value for x=0 is equal to the y-value of x=5. So when x=5, y=4.


Now lets make a table of the values we have calculated 



 xy


 04
 

 10
 

 2.5-2.25
 

 40
 

 54

Notice if you graph the equation y=x%5E2-5x%2B4 with the axis of symmetry you get
Graph of y=x%5E2-5x%2B4 through the given points. Notice the axis of symmetry is the equation x=2.5 which is the vertical line through the vertex of the parabola.