The vertex form of a quadratic equation is written as
y = a(x - h)^2 + k
where
h and k are the x and y coordinates of the vertex
The standard equation of a quadratic function is
ax^2 + bx + c = 0
The given equation is
y = x^2 + 8x + 7 = 0
By comparing,
a = 1, b = 8, c = 7
The formula for finding the x coordinate of the vertex is
x = - b/2a = 8/2*1 = 4
We would substitute x = - 4 into the equation to get y
y = (- 4)^2 + 8(4) + 7 = 16 - 32 + 7 = - 9
h = 4, k = - 9 , a = 1
By substituting,
y = (x - 4)^2 - 9
The second option is correct