SOLUTION: What is the value of c if the vertex of the parabola {{{y=x^2-8x+c}}} is a point one x-axis?

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Question 468343: What is the value of c if the vertex of the parabola y=x%5E2-8x%2Bc is a point one x-axis?
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
If the vertex is on the x_axis, then the y_value of vertex must be 0.
Vertex: (x_value, 0)
To determine x-value of vertex, use formula for finding line of symmetry
x+=+%28-b%29%2F2a
For the given parabola, a = 1, b = -8, c = c
x+=+8%2F2+=+4
Therefore the vertex is at (4,0)
To solve for c, plug in these values for x,y into given equation
y+=+x%5E2+-8x+%2Bc
0+=+4%5E2+-%288%29%284%29+%2B+c
0+=+16+-+32+%2B+c
0+=+-16+%2B+c
16+=+c
So value of c is 16.
Any other value other than 16 would yield a vertex not on the x-axis.