SOLUTION: I need to identify the axis of symmetry, create a suitable table of values and sketch a graph including the axis of symmetry for: y = x^2 - 5x +3 I know the formula to find the

Algebra ->  Graphs -> SOLUTION: I need to identify the axis of symmetry, create a suitable table of values and sketch a graph including the axis of symmetry for: y = x^2 - 5x +3 I know the formula to find the       Log On


   

Question 90223This question is from textbook Beginning Algebra
: I need to identify the axis of symmetry, create a suitable table of values and sketch a graph including the axis of symmetry for: y = x^2 - 5x +3
I know the formula to find the axis is x = -b/2a thus
x = -(-5)/2(1) = 5/2
From here on out I'm lost. I get really confused whenever fractions are involved. I'm not sure what numbers to choose for my values and why to choose those numbers.
Any help would be appreciate. This question is from textbook Beginning Algebra

Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
you've got the hard part ... for your table of values, choose numbers for x that are equally spaced around the axis of symmetry

like 2, 3, 1, 4, 0, 5 ... then plug these values into the original equation to get matching y values

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since you know the x-value of the vertex (which is 5%2F2) plug in x=5%2F2 to find the y value

y+=+%285%2F2%29%5E2+-+5%285%2F2%29+%2B3+plug in x=5%2F2


y+=+25%2F4+-+25%2F2+%2B3+ Multiply

y+=+25%2F4+-+50%2F4+%2B12%2F4+ Make into equivalent fractions with the common denominator

y+=+%2825-50%2B12%29%2F4+ Combine the fractions

y+=+-13%2F4+ combine the numerator

So the vertex is (5%2F2,-13%2F4) which is one point on our graph


Now plug in the x-values x=1,x=2,x=3,x=4 (notice x=1 and x=4 are the same distance from x=2.5, which is the axis of symmetry. Also x=2 and x=3 are the same distance from x=2.5.)



Lets evaluate f%281%29

f%28x%29=x%5E2-5x%2B3 Start with the given polynomial


f%281%29=%281%29%5E2-5%281%29%2B3 Plug in x=1


f%281%29=%281%29-5%281%29%2B3 Raise 1 to the second power to get 1


f%281%29=%281%29-5%2B3 Multiply 5 by 1 to get 5


f%281%29=-1 Now combine like terms


So our 1st point is (1,-1)



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



Lets evaluate f%282%29

f%28x%29=x%5E2-5x%2B3 Start with the given polynomial


f%282%29=%282%29%5E2-5%282%29%2B3 Plug in x=2


f%282%29=%284%29-5%282%29%2B3 Raise 2 to the second power to get 4


f%282%29=%284%29-10%2B3 Multiply 5 by 2 to get 10


f%282%29=-3 Now combine like terms


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



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



Lets evaluate f%283%29

f%28x%29=x%5E2-5x%2B3 Start with the given polynomial


f%283%29=%283%29%5E2-5%283%29%2B3 Plug in x=3


f%283%29=%289%29-5%283%29%2B3 Raise 3 to the second power to get 9


f%283%29=%289%29-15%2B3 Multiply 5 by 3 to get 15


f%283%29=-3 Now combine like terms


So our 3rd point is (3,-3)



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



Lets evaluate f%284%29

f%28x%29=x%5E2-5x%2B3 Start with the given polynomial


f%284%29=%284%29%5E2-5%284%29%2B3 Plug in x=4


f%284%29=%2816%29-5%284%29%2B3 Raise 4 to the second power to get 16


f%284%29=%2816%29-20%2B3 Multiply 5 by 4 to get 20


f%284%29=-1 Now combine like terms


So our 4th point is (4,-1)


Now lets make a table of the values we have calculated (note: I'm writing 5%2F2 as 2.5 and -13%2F4 as -3.25) 



 xy



 1-1
 

 2-3


 2.5-3.25
 

 3-3
 

 4-1


Notice how the x-values x=1 and x=2 have the same y value as x=3 and x=4. So to save time, you only need half of these points to make an adequate table (since the parabola is symmetrical)

Here you can see that the parabola is symmetrical about the axis of symmetry