SOLUTION: How do you graph Y = x2 -6x +8?

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Question 651391: How do you graph Y = x2 -6x +8?
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi,
How do you graph
Y = x^2 -6x +8 || Putting into Vertex Form by completing the Square
y =(x-3)^2 - 9 + 8
y = (x-3)^2 - 1 and when (x-3)^2 - 1 = 0 ,, x = 3 � 1
the vertex form of a Parabola opening up(a>0) or down(a<0),
where(h,k) is the vertex and x = h is the Line of Symmetry
Parabola opening Upward, V(3,-1) and x - 3 the line of symmetry
x-intercepts (2,0) and (4,0)

Answer by MathLover1(20849) (Show Source):
You can put this solution on YOUR website!

A parabola is of the general form , and you have that.
If is the parabola (looks like a smiley face), if is the parabola (looks like a sad face).
It is to note that for your question, you have the opposite , instead of , you goes up.
In case of will be on , and when this occurs, a positive value means it will go to the , so it will look like a letter .

first, you can do is to find the vertex using
...this is value...plug it in and find value

so, the vertex is at the point (,)

In this example you can factor to find the , the possible values for in our general form, when .
So,

........substitute with
...group
...factor out from first group and from second group
...set

if ..->...
if ..->...

So the parabola passes through the on the graph at and . As parabola are symmetrical, the of is halfway between these, ie .
So sub this value into the original equation to find the lowest point of the parabola.
...now set and solve for to find

...so, there is at the point (,)
you can also take few other positive and negative values for , calculate and plot that points too, and you are ready to draw a graph