As we can see from the graph, the vertex of this parabola lies at ( - 3, 4). By knowing these, we can use the Vertex Form of a quadratic function to write our equation. Let's remember it!
y = a(x- h)^2+ k
In this form a gives the direction of the parabola. When a>0 the parabola faces upward and when a<0 it faces downward. Moreover, ( h, k) represents the vertex of the parabola. Knowing this, let's substitute h= -3 and k= 4 into the above equation.
y = a(x-( - 3))^2+ 4
⇓
y = a(x+3)^2+4
Great! Now, we can eliminate the options F and G because they have different vertices. Next, let's consider the value of a. Since we know that our function opens downward, the value of a must be negative. Therefore, we can conclude that our only possible answer would be option H in the case of a= -1.
y = -(x+3)^2+4
