SOLUTION: Algebraically determine the point(s) of intersection between the following functions. f(x) = 2x^2+3 g(x) = −3x+8

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Question 1180506: Algebraically determine the point(s) of intersection between the following functions.
f(x) = 2x^2+3
g(x) = −3x+8
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
First step, f(x)=g(x)

Second step, 2x^2+3=-3x+8.

Continue from there.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29%E2%80%89=+2x%5E2%2B3
g%28x%29+=+-3x%2B8

first find x that makes f%28x%29%E2%80%89=g%28x%29
2x%5E2%2B3=+-3x%2B8
2x%5E2%2B3%2B3x-8=0
2x%5E2%2B3x-5=0...use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A2%2A%28-5%29+%29%29%2F%282%2A2%29+
x+=+%28-3+%2B-+sqrt%28+9%2B40+%29%29%2F4+
x+=+%28-3+%2B-+sqrt%28+49+%29%29%2F4+
x+=+%28-3+%2B-+7%29%2F4+
solutions:
x+=+%28-3+%2B+7%29%2F4+ =>x=1
x+=+%28-3+-+7%29%2F4+ =>x=-5%2F2

calculate y coordinate of the intersection point

f%28x%29%E2%80%89=+2%2A1%5E2%2B3
f%28x%29%E2%80%89=+5
one point of intersection between the following functions is: (1,5)
and
f%28x%29%E2%80%89=+2%2A%28-5%2F2%29%5E2%2B3
f%28x%29%E2%80%89=+31%2F2


second point of intersection between the following functions is: (-5%2F2,31%2F2)