Answer:
f(x) = -3(x -(-1))² +7
Explanation:
You want the equation of the quadratic function that matches the given table.
Look
The first step in solving the problem is to look at the given information. To use the given equation, you need to know the vertex of the function, and its vertical scale factor.
Vertex
A quadratic function is symmetrical about the line through its vertex. That means we can locate the vertex by looking for x-values where the y-value is the same. The x-value of the vertex is halfway between those x-values.
Here, f(x) = 4 for both x=-2 and x=0. That means the x-value of the vertex is ...
(-2 +0)/2 = -1
This value of x is in the table, and f(-1) is given as 7. This means the vertex is (-1, 7) and these are the values that go in the two rightmost boxes.
f(x) = ( )(x -(-1))² + 7
Scale factor
The scale factor in the first box can be found by considering the difference between the f(x) value at the vertex, and the f(x) value at a point that is 1 unit either side:
( ) = f(-2) -f(-1) = 4 -7 = -3
The scale factor is -3, so the equation is ...
f(x) = -3(x -(-1))² +7