Answer:
f(x) = x² +4x -12
Explanation:
You want the standard form equation of the quadratic represented by the values in the table.
Minimum
The table shows the minimum is -16 at x = -2. That is, the vertex is at (-2, -16).
The table also shows the function value increases by 1 to -15 when x is ±1 unit from its vertex value. That increase of 1 tells you the leading coefficient is 1.
Vertex form
The vertex form of a quadratic equation is ...
f(x) = a(x -h)² +k
where 'a' is the leading coefficient, and (h, k) is the vertex.
For this function, we have a=1, (h, k) = (-2, -16), so the vertex form of the equation is ...
f(x) = (x +2)² -16
Standard form
Expanding the vertex form equation, we get ...
f(x) = (x² +4x +4) -16
f(x) = x² +4x -12