SOLUTION: 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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Question 769550: 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.
Found 2 solutions by reviewermath, josgarithmetic:
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2+-2x-4 = 3x + 5
3x%5E2+-+5x+-+9 = 0
a = 3, b = -5, c = -9
discriminant, b%5E2+-+4ac = %28-5%29%5E2+-+4%283%29%28-9%29 = 133 > 0, therefore
there are two points of intersections.
Here's the graph:

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Finding points of intersection between the line and the parabola means we equate "y" and f(x):
3x%2B5=3x%5E2-2x-4
simplifying into 3x%5E2-2x-3x-4-5=0
3x%5E2-5x-9=0

Finding how many points can use the discriminant of that:
%28-5%29%5E2-4%2A3%2A%28-9%29
25%2B12%2A9
...only need to see that this value is positive.
Seeing the discriminant is positive, means 3x%5E2-5x-9 has TWO real roots, so this means TWO points of intersection between "y" and f(x).