The vertex form of a parabola is expressed as
y = a(x - h)^2 + k
where
a is the leading coefficient
h and k are the horizontal and vertical coordinates of the vertex.
Recall, the general expression for a quadratic equation is
y = ax^2 + bx + c
By comparing with the given equation,
a = - 2, b = 36, c = - 171
The formula for the x coordinate of the vertex is
x = - b/2a
x = - 36/(2 * - 2) = - 36/- 4 = 9
Substituting x = 9 into the equation, we have
y = - 2(9)^2 + 36(9) - 171
y =