Find the vertex of the parabola whose equation is y = x2 + 6x + 2.
Answer: The vertex of the given parabola is (-3, -7).
Step-by-step explanation: We are given to find the vertex of the parabola with the following equation :
\(y=x^2+6x+2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We know that
the vertex form of a parabola is given by
\(y=a(x-h)^2+k,\) where (h, k) is the vertex of the parabola.
From equation (i), we have
\(y=x^2+6x+2\\\\\Rightarrow y=(x^2+6x)+2\\\\\Rightarrow y=(x^2+2\times x\times3+3^2)+2-3^2\\\\\Rightarrow y=(x+3)^2+2-9\\\\\Rightarrow y=(x+3)^2-7\\\\\Rightarrow y=(x-(-3))^2+(-7).\)
Comparing the above equation with the vertex form, we get
vertex, (h, k) = (-3, -7).
Thus, the vertex of the given parabola is (-3, -7).