Answer: To write the quadratic function in vertex form, we use the general form:
f(x) = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola.
Given that the vertex is V(5, -4), we have h = 5 and k = -4. So the equation in vertex form is:
f(x) = a(x - 5)^2 - 4
Now, we need to find the value of 'a' to complete the equation. For this, we can use the point P(-1, 5) that the function passes through.
Substitute the coordinates of point P(-1, 5) into the equation:
5 = a(-1 - 5)^2 - 4
Simplify:
5 = a(-6)^2 - 4
5 = 36a - 4
Now, isolate 'a':
36a = 5 + 4
36a = 9
a = 9 / 36
a = 1/4
So, the value of 'a' is 1/4.
Now, we can write the final equation in vertex form:
f(x) = (1/4)(x - 5)^2 - 4