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Determine all points of intersection?
Show work/explain steps.
1. parabola y = x^2 + 3x - 4 and line y = 5x + 11
2. y = cos x and y = sin x in the first quadrant
1 Answer
- ?Lv 79 years agoFavorite Answer
1.
Substitute 5x + 11 for y in the other equation, and solve for x.
y = x^2 + 3x - 4
5x + 11 = x^2 + 3x - 4
x^2 - 2x - 15 = 0
(x - 5)(x + 3) = 0
x - 5 = 0 or x + 3 = 0
x = 5 or x = -3
Now find the y that corresponds to each x.
When x = 5, y = 5x + 11 = 5(5) + 11 = 36.
When x = -3, y = 5x + 11 = 5(-3) + 11 = -4
So the points of intersection are (5, 36) and (-3, -4).
2.
y = cos x and y = sin x
cos x = sin x
Solve for x.
This occurs at x = pi/4, where cos x = sin x = sqrt(2) / 2.
So the point of intersection is (pi/4, sqrt(2) / 2).
