Question

Which system of equations is represented by the graph?

Graph of a quadratic function intersecting a linear function at points 0 comma negative 1 and 3 comma 2.

y=x^2 -2x-1
x-y=1

y=x^2-2x+1
x+y=1

y=x^2-2x-1
x+y=1

y=x^2-2x+1
x-y=1

Answer 1

(a) y = x^2 -2x -1; x -y = 1

Explanation:

You want to know which system of equations has solutions (0, -1) and (3, 2).

Point (0, -1)

The linear equations are ...

• x -y = 1
• x +y = 1

Substituting this point into these equations, we have ...

• 0 -(-1) = 1 . . . . . true
• 0 +(-1) = 1 . . . . . false

This eliminates choices B and C.

The quadratic equations have constants of -1 or +1. For the point (0, -1) to satisfy the equation, the constant must be -1.

This eliminates choices B and D

The only viable choice is A:

• y = x^2 -2x -1
• x - y = 1