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