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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 + b
In 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).

Respuesta :

Edufirst
Parabola equation: y - 4 = (x -3)^2 => y = (x - 3)^2 + 4 => Vertex of the parabola = (3,4)

y = - x + b intersects at (3,4) => 4 = - 3 + b = b = 7.

Then y = - x + 7

Now you can find the second solution by making (x - 3)^2 + 4 = - x + 7

x^2 - 6x + 9 + 4 = - x + 7

x^2 -5x + 6 = 0

Factor to find the roots: (x - 3) (x - 2) =0 => x = 3 and x = 2

x = 3 corresponds to the vertex of the parabola, then the other intersection point is at x =2, for which y = -2 + 7 = 5. => point (2,5) and the answer is the first option: b equal 7 and a second solution to the system must be located at the point (2,5).

Answer:

THE ANSWER IS A

Step-by-step explanation:

JUST TOOK THE EXAM ITS A

GOOD LUCK

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