MATH SOLVE

2 months ago

Q:
# Tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola. Equation 1: (x β 3)2 = y β 4 Equation 2: y = -x + bIn order for this solution to be reasonable, which qualifications must be met?b must equal 7 and a second solution to the system must be located at the point (2, 5).b must equal 1 and a second solution to the system must be located at the point (4, 5).b must equal 7 and a second solution to the system must be located at the point (1, 8).b must equal 1 and a second solution to the system must be located at the point (3, 4).

Accepted Solution

A:

Answer:b must equal 7 and a second solution to the system must be located at (2, 5).Step-by-step explanation:Rearranging the first equation:y = (x - 3)^2 + 4From this we see that the vertex is at the point (3,4). So one solution of equation 2 is (3 ,4).Substituting in equation 2:4 = -3 + bb = 7.So equation 2 is y = - x + 7.Now we check if Β (2, 5) is on this line:5 = -2 + 7 = 5 , therefore Β (2, 5) is on this line.Verifying if (2, 5) Β is also on y = (x - 3)^2 + 4:5 = (2 - 3)^2 + 4 = Β 1 + 4 = 5- so it is. and a second solution to the system is (2, 5).