Question

How many times does the graph of the function below intersect the the x-axis? 16x^2-8x+1

Answer 1

Factor 16x2−8x+1
16x2−8x+1
=(4x−1)(4x−1)

Answer 2

(4x−1)(4x−1)

Answer 3

This can be written as\[(4x-2)^{2}-3\]
This will intersect x-axis two times.

Answer 4

Thanks.

Answer 5

your welcome

Answer 6

Does this relate to multiplicity rules?

Answer 7

You just need to evaluate the discriminant to find how many times the function hits the x-axis:
\(b^2 -4ac >0 \implies 2 \ \ sol \ \ or\ \ x-int\)
\(b^2-4ac = 0 \implies 1 \ \ sol \)
\(b^2-4ac < 0 \implies \ \ no \ \ sol\)

Answer 8

no solution