PLEASEE HURRY!!!!!!!! Tom determines that 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 – 4Equation 2: y = -x + bIn order for Tom’s thinking to be correct, which qualifications must be met? A: b must equal 7 and a second solution to the system must be located at the point (2, 5).B: b must equal 1 and a second solution to the system must be located at the point (4, 5).C: b must equal 7 and a second solution to the system must be located at the point (1, 8).D: b must equal 1 and a second solution to the system must be located at the point (3, 4).

Answer:Option A: b must equal 7 and a second solution to the system must be located at the point (2, 5)Step-by-step explanation:step 1Find the vertex of the quadratic equationThe general equation of a vertical parabola in vertex form is[tex]y=a(x-h)^2+k[/tex]where(h,k) is the vertexwe have[tex](x-3)^{2}=y-4[/tex]so[tex]y=(x-3)^{2}+4[/tex]The vertex is the point (3,4)step 2Find out the value of b in the linear equationwe know thatIf the vertex is a solution of the system of equations, then the vertex must satisfy both equationssubstitute the value of x and the value of y of the vertex in the linear equation[tex]y=-x+b[/tex]For x=3, y=4[tex]4=-3+b[/tex][tex]b=7[/tex]so[tex]y=-x+7[/tex]step 3Find out the second solution of the system of equationswe have[tex]y=(x-3)^{2}+4[/tex] -----> equation A[tex]y=-x+7[/tex] ----> equation Bsolve the system of equations by graphingRemember that the solutions are the intersection points both graphsThe second solution of the system of equations is (2,5)see the attached figurethereforeb must equal 7 and a second solution to the system must be located at the point (2, 5)