Question

What is the equation of the graph below?

Answer 1

ANSWER


`f(x) = (x + 3)^(2) - 1`



Step-by-step explanation

The vertex of the graph is at



`(-3,-1)`


The equation of the graph in vertex form is given by the formula,




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


The above graph has a minimum point, hence

`a > \: 0`

When we put these values into the equation we obtain,


`f(x) = a(x - - 3)^(2) + - 1`


This implies that,


`f(x) = a(x + 3)^(2) - 1`

The point (-2,0) lies on the line.



`a( - 2 + 3)^(2) - 1 = 0`


`a = 1`



`f(x) = (x + 3)^(2) - 1`

The correct answer is D.