Question

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

Oy=(-12+1
O y--1-
O y=(«+ 1) +1
O y=x+1)-1

Answer 1

`y = (x +1)^2 - 1`

Explanation:

Given

`Vertex = (-1,-1)`

Required

Determine the equation

The equation of a graph from a vertex is:

`y = a(x - h)^2 + k`

Where

`a = 1`

`(h,k) = (-1,-1)`

Substitute these values in
`y = a(x - h)^2 + k`

`y = 1(x - (-1))^2 + (-1)`

Express -(-1) as 1

`y = 1(x +1)^2 + (-1)`

Express +(-1) as -1

`y = 1(x +1)^2 - 1`

`y = (x +1)^2 - 1`

Hence, the equation is:

`y = (x +1)^2 - 1`