Question

Identify the graph that has a vertex of (1,-1) and a leading coefficient of a=2.

Answer 1

`f(x) = 2 ({x - 1)}^(2) - 1`

Step-by-step explanation

The vertex form of a parabola has equation:

`f(x) = a ({x - h)}^(2) + k`

where V(h,k) is the vertex of the parabola and 'a' is the leading coefficient.

From the question, we have that, the vertex is

`(1,-1)`

and the leading coefficient is

`a= 2`

We substitute the vertex and the leading coefficient into the vertex form to get:

`f(x) = 2 ({x - 1)}^(2) + - 1`

We simplify to get:

`f(x) = 2 ({x - 1)}^(2) - 1`

The graph of this function is shown in the attachment.