Answer:
(-4, -4)
Step-by-step explanation:
A quadratic equation \(y = ax^2+bx+c\) has written in vertex form using the completing square method is:
\(y = a(x-h)^2+k\)
where, (h, k) is the vertex
As per the statement:
\(y = x^2 + 8x + 12\)
Using the completing square method we have;
\(y = x^2 + 8x + 12+(\frac{8}{2} )^2-(\frac{8}{2} )^2\)
⇒\(y =x^2+8x+12+4^2-4^2\)
Using identity rule:
\((a+b)^2 = a^2+2ab+b^2\)
then;
\(y=(x+4)^2+12-16\)
⇒\(y =(x+4)^2-4\)
vertex of the given equation is: (h, k) = (-4, -4)
Therefore, the vertex of the parabola whose equation \(y = x^2 + 8x + 12\) is (-4, -4)
