Question

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

Answer 1

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).

Answer 2

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`