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}}}

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?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the axis of symmetry, use this formula:

From the equation we can see that a=1 and b=-5

Plug in b=-5 and a=1

Negate -5 to get 5

Multiply 2 and 1 to get 2

So the axis of symmetry is

So the x-coordinate of the vertex is (which is in decimal form). Lets plug this into the equation to find the y-coordinate of the vertex.

Lets evaluate

Start with the given polynomial

Plug in

Raise 2.5 to the second power to get 6.25

Multiply 5 by 2.5 to get 12.5

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

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

Lets evaluate

Start with the given polynomial

Plug in

Raise 0 to the second power to get 0

Multiply 5 by 0 to get 0

Remove any zero terms

So our 1st point is (0,4)

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

Lets evaluate

Start with the given polynomial

Plug in

Raise 1 to the second power to get 1

Multiply 5 by 1 to get 5

Now combine like terms

So our 2nd point is (1,0)

Now remember, the parabola is symmetrical about the axis of symmetry (which is )
This means the y-value for is equal to the y-value of . So when , .
Also, the y-value for is equal to the y-value of . So when , .

Now lets make a table of the values we have calculated

Notice if you graph the equation with the axis of symmetry you get
Graph of through the given points. Notice the axis of symmetry is the equation which is the vertical line through the vertex of the parabola.
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