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contestada

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

Respuesta :

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

[tex]y=a(x-h)^{2} +k[/tex]

where

[tex](h,k)[/tex] is the vertex of the parabola

case A) [tex]y=(x-1)^{2} +1[/tex]

In the case A) the vertex is the point [tex](1,1)[/tex]

Therefore

the case A) is not the solution of the problem

case B) [tex]y=(x-1)^{2} -1[/tex]

In the case B) the vertex is the point [tex](1,-1)[/tex]

Therefore

the case B) is not the solution of the problem

case C) [tex]y=(x+1)^{2}+1[/tex]

In the case C) the vertex is the point [tex](-1,1)[/tex]

Therefore

the case C) is not the solution of the problem

case D) [tex]y=(x+1)^{2}-1[/tex]

In the case D) the vertex is the point [tex](-1,-1)[/tex]

Therefore

the case D) is the solution of the problem

the answer is the option D

[tex]y=(x+1)^{2}-1[/tex]




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