Help me please?

To find the answer without drawing the graph of the equation, we must factor and solve for x.

y=16x^2-8x+1
y=(4x-1)(4x-1)

Now plug in 0 for y (because if y is 0 then that means the line is crossing the x-axis at the corresponding x -- think about the graph), break up the factors, and solve for both x terms.

0=4x+1 and 0=4x+1
x=-1/4 and x=-1/4

The two x values are the same, so the graph of y=16x^2-8x+1 crosses the x-axis only at -1/4.

Your answer is 1.

Compute the discriminant:
d = b² - 4ac
d = (-8)² - 4(16)(1)
d = 64 - 64
d = 0

Since it is zero, that means there is 1 real (double) root.

Answer:
B. 1

f(x) = y = (4x -1)^2
f has only one zero, at x = 1/4.
Since the term is squared, it has a zero of multiplicity two, but it has just that one point of intersection with the x-axis.

y = 16x² - 8x + 1
discriminant = (-8)² - 4·16·1 = 0
Since the discriminant is 0, the graph touches the x-axis at one point.

C. 2