The system of equations represented by the attached graph is y = (x + 3)^2 - 2 and y = -x + 1
How to determine the system of equations?
This question will be answered using the attached graph
The curve
The curve is a quadratic function, and it has the following features:
Vertex, (h, k) = (-3, -2)
Point (x, y) = (-1, 2)
A quadratic function is represented as:
y = a(x - h)^2 + k
So, we have:
y = a(x + 3)^2 - 2
Substitute (x, y) = (-1, 2)
2 = a(-1 + 3)^2 - 2
This gives
2 = 4a-2
Solve for a
a = 1
Substitute a = 1 in y = a(x + 3)^2 - 2
y = (x + 3)^2 - 2
The line
The line is a linear function, and it has the following features:
Point (x1, y1) = (-1, 2)
Point (x2, y2) = (-6, 7)
The linear function is calculated as:
y = (y2 - y1)/(x2 - x1) *(x- x1) + y1
So, we have:
y = (7 -2)/(-6 +1) *(x + 1) + 2
Evaluate the quotient
y = -1(x + 1) + 2
Expand
y = -x -1 + 2
y = -x + 1
Hence, the system of equations represented by the attached graph is y = (x + 3)^2 - 2 and y = -x + 1
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