Question 468343
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 = (-b)/2a}}}
For the given parabola, a = 1, b = -8, c = c
{{{x = 8/2 = 4}}}
Therefore the vertex is at (4,0)
To solve for c, plug in these values for x,y into given equation
{{{y = x^2 -8x +c}}}
{{{0 = 4^2 -(8)(4) + c}}}
{{{0 = 16 - 32 + c}}}
{{{0 = -16 + c}}}
{{{16 = c}}}
So value of c is 16.
Any other value other than 16 would yield a vertex not on the x-axis.