Question 769550
Q:
Use the discriminant to determine the number of points of intersection on the line y= 3x +5 and the quadratic function f(x) = 3x^2 -2x-4
Solve to find the points of intersection. 
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A:
{{{3x^2 -2x-4}}} = 3x + 5
{{{3x^2 - 5x - 9}}} = 0
a = 3, b = -5, c = -9
discriminant, {{{b^2 - 4ac}}} = {{{(-5)^2 - 4(3)(-9)}}} = 133 > 0, therefore
there are two points of intersections.
Here's the graph:
{{{drawing(500,500,-15,15,-15,15,grid(1),graph(500,500,-15,15,-15,15,3x^2-2x-4,3x+5))}}}