How do you find the axis of symmetry for a quadratic equation #y = x^2 + 6x + 13#?

1 Answer
Jun 5, 2015

The axis of symmetry of a quadratic equation is the line parralel to the #Oy# axis passing through the vertex of the parabola. Therefore, we need the #x_v# coordinate of the vertex. #V(x_v, y_v)#

For a quadratic equation #f(x)=ax^2 + bx +c#, we have the following formulae for the coordinates of the vertex:
#x_v=-b/(2a)# and # y_v= -Delta/(4a)#, where #Delta = b^2-4ac#

Therefore, # x_v= -6/(2*1)=-3#

So, the axis of symmetry of the equation #y=x^2+6x+13# is the line defined by the equation #x=-3#.

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