SOLUTION: Find the vertex of the parabola represented by this equation: {{{y = (x-2)(x-6)}}}

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the vertex of the parabola represented by this equation: {{{y = (x-2)(x-6)}}}       Log On


   

Question 313085: Find the vertex of the parabola represented by this equation:
y+=+%28x-2%29%28x-6%29
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You did get the value correct for x=-2.
But that point is not the vertex.
To get to vertex form, complete the square.
y=x%5E2-8x%2B12
y=%28x%5E2-8x%2B16%29-4
y=%28x-4%29%5E2-4
THe equation is now in vertex form,
y=a%28x-h%29%5E2%2Bk
where (h,k) is the vertex.
For your equation, the vertex is (4,-4).
Here's a graph to verify.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2-8x%2B12%29

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

y+=+%28x-2%29%28x-6%29
y+=+x%5E2-2x-6x%2B12
y+=+x%5E2-8x%2B12
a=1, b=-8, c=12
x-coordinate of vertex = -b%2F%282a%29=-%28-8%29%2F%282%2A1%29=-%28-4%29=4
The y-coordinate of the vertex is found by substituting x=4 into
y+=+x%5E2-8x%2B12
y+=+%284%29%5E2-8%284%29%2B12
y=16-32%2B12
y=-4
So the vertex is the point (4,-4).
Edwin