Algebra problem

Question

Graph the parabola. Label the vertex.

f(x) = -x² - 2x - 6

Answer 1

Please see response from Mark M.

Answer 2

The graph of y = a(x-h)²+k is a parabola with vertex (h,k).  If a>0, the parabola opens upward and the vertex is the lowest point on the graph. If a<0, the graph opens downward and the vertex is the highest point.  

 

Put the given equation into the form y = a(x-h)²+k by completing the square:

 

  y = -x² - 2x - 6

 

     = -(x²+2x) - 6

 

     = -(x²+2x+1-1)-6

 

 y = -(x+1)² - 5

 

The parabola opens downward with vertex (highest point) (-1,-5).