Question

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

Answer 1

ANSWER

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

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.