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What are the points of intersection of the following parabolas y equals x2 -7x plus 8 and y equals -x2 plus 9x -6?
Wiki User
∙ 11y ago
y = x2 - 7x + 8 y = -x2 + 9x - 6 subtract the 2nd from the 1st equation
0 = 2x2 - 16x + 14 simplify
0 = x2 - 8x + 7 factor it, since 7 = (-1)(-7) and -1 - 7 = -8
0 = (x - 1)(x - 7) let each factor equal to zero
x - 1 = 0 or x - 7 = 0 solve for x
thus, x = 1 and x = 7.
Chose one of the equation and substitute x with 1, and 7 to find the corresponding y-values.
y = x2 - 7x + 8
y = (1)2 - 7(1) + 8 = 1 - 7 + 8 = 2; (1, 2) intersection point
y = (7)2 - 7(7) + 8 = 49 - 49 + 8 = 8; (7, 8) intersection point
Wiki User
∙ 11y ago
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False
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