Pre Calculus
posted by Jack on .
Determine the coordinates of the point (xy) where the curves y=(12)x−5 and y=x2+2x−15 intersect in the third quadrant

y = 12x  5. y = x^2 + 2x  15.
Substitute 12x  5 for y in the 2nd Eq:
12x 5 = x^2 + 2x 15,
Solve for x,
12x  x^2  2x = 15 + 5,
Combine liketerms:
x^2 + 10x + 10 = 0,
Multiply each side by 1:
x^2  10x  10 = 0,
Use quadratic formula to solve for x:
x = (10 + sqrt(100+40)) / 2,
x = 10.92 , 0.916,
x = 0.916(3rd quadrant).
Substitute 0.916 for x in 1st Eq:
y = 12 * 0.916  5 = 16.
P(0.916 , 16) 
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