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Question 734089: Complete the square in graphing form: y = x^2 - 7x + 5?
How to solve this? I think I can used the quadratic formula to solve it but I'm a bit confused. I think there are a few ways to solve this. I searched and found this on Yahoo.
http://answers.yahoo.com/question/index?qid=20090806151908AAkOA70
I followed these step by step from this person. It still confuses me and I think this person made a mistake too. Here is what I got so far with mine just by following this person's step by step tips.
y = x^2 - 7x + 5
I moved the 5 over to the other side like he did and got this. Moving it would make turn it into a negative number.
y - 5 = x^2 - 7x
Now to take 7 divide that in half which give us 3.5
Now we take that and square root it. It comes out to be 12.25
So now we are here.
y - 5 + 12.25 = x^2 - 7x + 12.25
Then
y + 7.25 = x^2 - 7x + 12.25
and following the steps that turns out to be this.
y + 7.25 = (x-3.5)^2
This is where I get all confused from this point on. I learned from asking on Yahoo that the 12.25 remaining on the right side is not needed. I can just dropped that. Now I have to move the 7.25 from the left side, which used to be a -5, to the right side again. As before when I changed the 5 to a -5 when I moved it from the right to the left, do I change it again as I move it to the right?
It should end up being this.
y = (x-3.5)^2 - 7.25
Right? More confused now. Following his steps on Yahoo, I found out that the Vertex is (3.5, -7.25). I'm guessing the -3.5 in the equation changes into a positive and the -7.25 stay the same. How do I graph it and how do I solve the remaining. I Google the equation and it show me the graph. It's turns out being a U shape on the graph but I don't know where I should put all the points on the line.
Sun
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Complete the square in graphing form: y = x^2 - 7x + 5?
.
The idea to keep in mind is that the "vertex form" of a quadratic is:
y = a(x – h)^2 + k
where
(h,k)is the vertex
.
y = x^2 - 7x + 5
since the y is already in the correct position, complete the square ONLY on the right side:
y = x^2 - 7x + 5
group x's:
y = (x^2 - 7x) + 5
add (b/2)^2 to the inside of the () and balance by subtracting on the outside:
y = (x^2 - 7x+12.25) + 5-12.25
y = (x-3.5)^2-7.25
from "y = a(x – h)^2 + k"
we see that the vertex is:
(3.5, -7.25)
.
First point on the graph (i.e., the lowest point on the graph)
.
To find y-intercepts, set x=0 and solve for y:
y = (x-3.5)^2-7.25
y = (0-3.5)^2-7.25
y = (-3.5)^2-7.25
y = 12.25-7.25
y = 4.75
Second point is at (0, 4.75)
.
To find x-intercepts, set y=0 and solve for x:
0 = (x-3.5)^2-7.25
7.25 = (x-3.5)^2
take the square root of both sides:
sqrt(7.25) = x-3.5
+-sqrt(7.25)+3.5 = x
6.24 = x
and
0.81 = x
.
Third point is at (6.24,0)
Fourth point is at (.81,0)
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