Question

What is the equation of the graph below?

Answer 1

ANSWER

$f(x) = (x + 3)^{2} - 1$



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.