Find the vertex, line of symmetry, and the max/min value of f(x). Graph the function.

f(x)=-3(x+1)^2+3

To find the vertex, line of symmetry, and the maximum/minimum value of the function f(x) = -3(x+1)^2 + 3, we can use the vertex form of a quadratic function, which is given by f(x) = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.

Comparing the given function f(x) = -3(x+1)^2 + 3 with the vertex form, we can see that a = -3, h = -1, and k = 3.

The vertex of the function will be given by the values (h, k), so the vertex is (-1, 3). This means that the graph of the function opens downwards and its vertex is located at (-1, 3) on the coordinate plane.

The axis of symmetry is a vertical line that divides the graph into two symmetrical halves. The equation for the line of symmetry is x = h, where h is the x-coordinate of the vertex. In this case, the equation for the line of symmetry is x = -1.

Next, to find the maximum/minimum value of the function, we can look at the coefficient of the x^2 term (a). Since a = -3 is negative, the parabola opens downwards, which indicates that the graph has a maximum point. The y-coordinate of the vertex (k) represents the maximum/minimum value of the function. Therefore, the maximum value of f(x) is 3.

Now, let's graph the function to visualize it.

Here is the graph of f(x) = -3(x+1)^2 + 3:

```
5|
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-3 -2 -1 0 1 2 3 4 5

```

In the graph, the vertex is (-1, 3), which is the highest point on the parabola. The axis of symmetry is the vertical line x = -1. The maximum value of the function f(x) is 3.