At how many points does the graph of the function below intersect the x-axis?
y = 2x2 - 3x + 1
a.2
b.1
c.0

Y=2x²-3x+1
one way is to find the zeroes
when it intersects the x axis, y=0
so
0=2x²-3x+1
solve for values of x that work
factor
0=(2x-1)(x-1)
set each to 0
we don't need to
we can see we have 2 different points that intersect

answer is A. 2

another way is to use the discriminant
b²-4ac
for ax²+bx+c=y
if the discriminant is
less than 0, then 0 intersections
equal to 0, then 1 intersection
greater than 0, then 2 intersection points

ax²+bx+c
2x²-3x+1
b²-4ac=(-3)²-4(2)(1)=9-8=1,
greater than 0
2 intersection points

answer is A