Question

At how many points does the graph of the function below intersects the x-axis?

Answer 1

Answer: 2 points

Step-by-step explanation: the graph of y=3x^2-5x+1 intersect the x-axis at those real values of x where y=0

i.e. 3x^2-5x+1=0

ax²+bx+c=0 has real roots if b²-4ac≥0

if b²-4ac=0 implies real and equal roots

here a=3,b=-5 and c=1

b²-4ac=25-12>0

this implies that this equation has unequal real roots

so,this equation will intersect the x-axis at two distinct points

Answer 2

Unfortunately it doesn't factor nicely.  You can try completing the square but it's really hard because A isn't 1.  Because A is positive, you know that the parabola opens upwards.  That means if you can find a negative function value then it definitely crosses the x axis twice because of symmetry.   If you plug in 1 for x then y is -1.  So the answer is C. 2.