Use the graph of the quadratic function f to write its formula as

f(x) = a(x – h)^{2} +k.

**Solution:-**

First determine the value of a, h, and k in f(x) = a(x – h)^{2}+k.

Recall that the coordinates of the vertex x and y correspond to the values of h and k.

Identify the vertex of the given parabola.

Vertex = (-1, 4)

The vertex is (-1,4). Thus h = -1 and k = 4. Now substitute values of h and k in f(x) = a(x-h)^{2} + k.

f(x) = x(x+1)^{2} + 4

To find a, substitute the coordinates of a point on the graph in the equation and solve for a. Selection any point on the graph of f other than the vertex.

Consider the point(0, -2). The point (0,-2)lies on the graph, so f(0) = -2.

f(x) = a(x + 1)^{2} + 4

let x = 0 and f(0) = -2.

-2 = a(0+1)^{2} + 4

-2 = a + 4

-6 = a

Finally, substitute a into the equation

f(x) = a(x + 1)^{2}+ 4.

f(x) = -6(x + 1)^{2} + 4