Question

Select the correct answer. Which system of equations is represented by this graph? A graph has two diagonal curves. A curve declines through (negative 1, 5), and (2 point 3, negative 5). A curve declines through (negative 5, negative 2) and (2 point 3, negative 5). Both curves intersect at (2 point 3, negative 5). A. B. C. D.

Answer 1

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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