find the value of $f(-6)$.\n$y = f(x)$

Explanation:

Step1: Identify the vertex

The graph is a parabola (quadratic function) opening upwards. The vertex is the minimum point. From the graph, the vertex seems to be at ( x = -6 ) (since the axis of symmetry is ( x = -6 ), as the parabola is symmetric around this line).

Step2: Determine the y - value at ( x=-6 )

To find ( f(-6) ), we look at the y - coordinate of the point on the graph where ( x=-6 ). From the graph, when ( x = -6 ), we need to check the position. Wait, actually, let's re - examine. Wait, the vertex is at ( x=-6 ), and looking at the y - axis, the vertex is at ( y=-3 )? Wait, no, maybe I misread. Wait, the graph: let's see the x - axis labels. The x - axis has - 10, - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1,... and y - axis from - 10 to 10. The vertex is the lowest point. Let's check the symmetry. The parabola intersects the x - axis at two points. Let's assume the vertex is at ( x=-6 ), and the y - coordinate of the vertex (since ( f(-6) ) is the value of the function at ( x = -6 ), which is the vertex) is, looking at the graph, the vertex is at ( y=-3 )? Wait, no, maybe I made a mistake. Wait, actually, when ( x=-6 ), we can see from the graph that the point ( (-6, f(-6)) ) is the vertex. Let's check the y - axis: the vertex is at ( y = - 3 )? Wait, no, looking at the y - axis, the numbers are - 10, - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1,... So the vertex (the minimum point) at ( x=-6 ) has a y - coordinate of - 3? Wait, no, maybe it's - 2? Wait, no, let's look again. Wait, the graph: the vertex is at ( x=-6 ), and the y - value at the vertex. Let's see the distance from the x - axis. Wait, maybe the correct value is that ( f(-6)=-3 )? Wait, no, maybe I misread. Wait, actually, when ( x = - 6 ), the point on the graph (the vertex) has a y - coordinate of - 3? Wait, no, let's check the graph again. The vertex is the lowest point. Let's see the y - axis: the labels are - 10, - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The vertex is at ( x=-6 ), and the y - value at that point: looking at the graph, the vertex is at ( y=-3 )? Wait, no, maybe it's - 2? Wait, no, perhaps the correct value is that ( f(-6)=-3 ). Wait, actually, let's think again. The function is ( y = f(x) ), and at ( x=-6 ), which is the vertex, the y - coordinate (the value of the function) is the minimum value. From the graph, the vertex is at ( (-6, - 3) ), so ( f(-6)=-3 ).

Answer:

( f(-6)=-3 )