Answer:
f(x) = 3(x +4)² -6
Explanation:
You want the equation for the parabola shown in the graph with vertex (-4, -6) and additional point (-5, -3).
Vertex form
The vertex form of the equation for a parabola is ...
f(x) = a(x -h)² +k
where the vertex is (h, k) and 'a' is the vertical scale factor.
Application
The vertex is shown on the graph as (h, k) = (-4, -6), so the equation will be of the form ...
f(x) = a(x +4)² -6
The value of 'a' is chosen to make the other given point lie on the graph. Substituting for (x, f(x)), we have ...
-3 = a(-5 +4)² -6
a = 3 . . . . . . . . . . . add 6
The equation of the graph is ...
f(x) = 3(x +4)² -6
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Additional comment
The point (-5, -3) is 1 unit horizontally and +3 units vertically from the vertex. When the point is 1 horizontal unit away from the vertex, that vertical difference (+3) is the scale factor 'a' in the vertex form equation.
In short, you don't need to solve the equation as we did above, you can read 'a' from the graph.