Question 769550
Finding points of intersection between the line and the parabola means we equate "y" and f(x):

{{{3x+5=3x^2-2x-4}}}
simplifying into {{{3x^2-2x-3x-4-5=0}}}
{{{3x^2-5x-9=0}}}


Finding how many points can use the discriminant of that:
{{{(-5)^2-4*3*(-9)}}}
{{{25+12*9}}}
...only need to see that this value is positive.
Seeing the discriminant is positive, means {{{3x^2-5x-9}}} has TWO real roots, so this means TWO points of intersection between "y" and f(x).