Question 1198798
we use the vertex form equation.

f(x) = a(x - h)^2 + k

where (h, k) represents the coordinates of the vertex.

Given the vertex (-1, 6), we substitute the values into the equation:

f(x) = a(x - (-1))^2 + 6

Simplifying further:

f(x) = a(x + 1)^2 + 6

 using the given point (0, 4).

Substitute x and f(x) into the equation:

4 = a(0 + 1)^2 + 6

4 = a(1)^2 + 6

4 = a + 6

a = -2

 substitute  'a' back into the equation:

f(x) = -2(x + 1)^2 + 6

So, the equation in vertex form is f(x) = -2(x + 1)^2 + 6.

*[illustration parabola1.png].