SOLUTION: What is the vertex of y=(2x-3)(2x+1). I'm confused on what to do when there's a number in front of the x

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Question 830385: What is the vertex of y=(2x-3)(2x+1). I'm confused on what to do when there's a number in front of the x
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The vertex occurs for the x value between the roots, exactly in the middle.

The x intercepts are considered to be the roots.
(2x-3)(2x+1)=0
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2x-3=0, then x=3%2F2 is one root
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2x+1=0, then x=-1%2F2 is a root.
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The x value at the exact middle of these is x=%28%283%2F2%29%2B%28-1%2F2%29%29%2F2=1%2F2
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What is the y coordinate where x=1%2F2?
Now you have your vertex, (x,y).
(Use the given equation for x=1%2F2 to find the corresponding y value).


graph%28300%2C300%2C-2%2C2%2C-5%2C1%2C%282x-3%29%282x%2B1%29%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
What is the vertex of y=(2x-3)(2x+1). I'm confused on what to do when there's a number in front of the x
y = (2x - 3)(2x + 1)

y+=+4x%5E2+-+4x+-+3 ------ FOILing the binomials

x+=+-+b%2F2a ------ Formula for the x-coordinate of the vertex, with:

a being + 4, and b being - 4 

x+=+-+%28-+4%29%2F2%284%29 ------- Determining x-coordinate of vertex

x, or x-coordinate of vertex = -+%28-+4%2F8%29, or 1%2F2



y+=+4%281%2F2%29%5E2+-+4%281%2F2%29+-+3 ----- Substituting 1%2F2 for x in quadratic equation 

y+=+4%281%2F4%29+-+4%2F2+-+3

y+=+1+-+2+-+3, or y+=+-+4

Vertex: (highlight_green%281%2F2%29,highlight_green%28-+4%29)

You can do the check!! 



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