Question 617138
{{{y=16x^-8x+1}}}
Places where a graph crosses the x axis are called x intercepts. Points on the x axis have a y coordinate of 0. So to find these points you set y = 0:
{{{0=16x^-8x+1}}}
Now we factor (or use the Quadratic Formula). This will factor according to the {{{a^2 -2ab + b^2 = (a-b)^2}}} pattern with the "a" being 4x and the "b" being a 1:
{{{0 = (4x-1)^2}}}
According to the Zero Product Property a product is zero only if a factor is zero. So:
4x - 1 = 0
Solving this we get:
{{{x = 1/4}}}<br>
So there is only one x intercept: (1/4, 0). And the answer to the question is: Once.