3

y = -x + 7

y = -0.5(x - 3)^2 + 8

replace y in the second equation:

-x + 7 = -0.5(x - 3)^2 + 8

-x + 7 = -0.5(x^2 - 6x + 9) + 8

-x + 7 = -0.5x^2 + 3x - 4.5 + 8

0.5x^2 - x - 3x + 7 + 4.5 - 8 = 0

0.5x^2 - 4x + 3.5 = 0

multiple 2 on both sides:

x^2 - 8x + 7 = 0

(x - 1)(x - 7) = 0

x = 1 or x = 7

y = -1 + 7 = 6 or y = -7 + 7 = 0

The solution for the system of equations y = -x + 7 and y = -0.5(x - 3)^2 + 8 is (1, 6), (7, 0)

Added 4/13/2014 7:33:01 PM

This answer has been confirmed as correct and helpful.

Confirmed by

jeifunk [4/13/2014 7:38:27 PM]

1

y = -x + 7 and y = -0.5(x - 3)2 + 8

Use equation 1 minus equation 2 we get

-x+7+0.5(x-3)^2-8=0

=> -x+7 +0.5(x^2 -6x+9) -8=0

=> -x -1 + 1/2x^2 -3x + 9/2=0

=> 1/2x^2 -4x+ 7/2=0

=> x=7 or x= 1

At x=7 we have y=-7+7 =0

At x=1 we have y=-1+7=6

The answer are ( 7,0) and (1,6)

Added 4/14/2014 2:04:32 PM

This answer has been flagged as incorrect.