Asked by trix(:
Solve the following system algebraically. Verify the solution
y=(1/2)(x-3)^2+4
y=-(1/2)(x-1)^2+6
y=(1/2)(x-3)^2+4
y=-(1/2)(x-1)^2+6
Answers
Answered by
oobleck
just equate the two expressions, since the y needs to be the same
(1/2)(x-3)^2+4 = -(1/2)(x-1)^2+6
(x-3)^2 + 8 = -(x-1)^2 + 12
x^2 - 6x + 9 + 8 = -x^2 + 2x - 1 + 12
2x^2 -8x +6 = 0
x^2-4x+3 = 0
(x-1)(x-3) = 0
(1/2)(x-3)^2+4 = -(1/2)(x-1)^2+6
(x-3)^2 + 8 = -(x-1)^2 + 12
x^2 - 6x + 9 + 8 = -x^2 + 2x - 1 + 12
2x^2 -8x +6 = 0
x^2-4x+3 = 0
(x-1)(x-3) = 0