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).
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 1
Find the vertex of the quadratic equation
The general equation of a vertical parabola in vertex form is where (h, k) is the vertex we have so , the vertex is the point (3,4)
step 2
Find out the value of b in the linear equation we know that if the vertex is a solution of the system of equations, then the vertex must satisfy both equations substitute the value of x and the value of y of the vertex in the linear equation for x=3, y=4.
step 3
Find out the second solution of the system of equations we have
-----> equation A
----> equation B
Solve the system of equations by graphing . Remember that the solutions are the intersection points both graphs . The second solution of the system of equations is (2,5)
Therefore , b must equal 7 and a second solution to the system must be located at the point (2, 5)
