Question

tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola. equation 1: (x – 3)2 = y – 4 equation 2: y = -x bin order for this solution to be reasonable, which qualifications must be met?

Answer 1

( x -3 )² = y - 4
y = ( x - 3 )² + 4
One solution is located at the vertex: ( 3, 4 ).
y = - x + b
4 = - 3 + b
b = 7
( x - 3 )² = - x + 7 - 4
x² - 6 x + 9 = - x + 3
x² - 5 x + 6 = 0
x² - 2 x - 3 x + 6 = 0
x ( x - 2 ) - 3 ( x - 2 ) = 0
( x - 2 ) ( x - 3 ) = 0
x 1 = 2,  x 2 = 3
y 1 = 5,  y 2 = 4.
In order for this solution to be reasonable, the 2nd equation must be:
y = - x + 7