Question

Tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola.

Answer 1

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 + 4

From 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 + b

b = 7.

So equation 2 is y = - x + 7.

Now we check if  (2, 5) is on this line:

5 = -2 + 7 = 5 , therefore  (2, 5) is on this line.

Verifying if (2, 5)  is also on y = (x - 3)^2 + 4:

5 = (2 - 3)^2 + 4 =  1 + 4 = 5

- so it is. and a second solution to the system is (2, 5).