Question

PLEASE HELP!!
At how many points does the graph of the function below intersect the x-axis?
y=4x^2-6x+1

a. 0
b. 1
c. 2
please show me how to solve it

Answer 1

When the function intersects the x-axis, y has to be 0. \[y=0\] So you insert that, and solve the equation:
\[4x^2-6x+1=0\]

Answer 2

The general formula for solving x here is: \[\frac{ -b \pm \sqrt{D} }{ 2a }\], where \[D=b^2-4ac\]

Answer 3

And actually, since you only need to find how many solutions there is, then you just need to solve D. If D is greater than 0, then there is two solutions, if it is equal to 0 there is one solution, and if its below 0 there is zero solutions.