raymongon1226
Answered

Which equation has a graph that is a parabola with a vertex at (–1, –1)?

A.y = (x – 1)2 + 1

B.y = (x – 1)2 – 1

C.y = (x + 1)2 + 1

D.y = (x + 1)2 – 1

Verified Answer :

Kalahira

The answer is y=(x+1)2-1. The x plus one causes the whole parabola to actually shift to the left by one unit rather than to the right. The subtraction of one causes a vertical shift down by one unit, so the vertex moves from (0,0) to (-1,-1).

calculista

Let's verify each case to determine the solution to the problem

we know that

The equation of the vertical parabola is of the form

\(y=a(x-h)^{2} +k\)

where

\((h,k)\) is the vertex of the parabola

case A) \(y=(x-1)^{2} +1\)

In the case A) the vertex is the point \((1,1)\)

Therefore

the case A) is not the solution of the problem

case B) \(y=(x-1)^{2} -1\)

In the case B) the vertex is the point \((1,-1)\)

Therefore

the case B) is not the solution of the problem

case C) \(y=(x+1)^{2}+1\)

In the case C) the vertex is the point \((-1,1)\)

Therefore

the case C) is not the solution of the problem

case D) \(y=(x+1)^{2}-1\)

In the case D) the vertex is the point \((-1,-1)\)

Therefore

the case D) is the solution of the problem

the answer is the option D

\(y=(x+1)^{2}-1\)




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