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

Answer 1

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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Answer 2

Ethan Adkins

To find the axis of symmetry for a quadratic equation in the form (y = ax^2 + bx + c), you use the formula:

[x = \frac{-b}{2a}]

For the equation (y = x^2 + 6x + 13), (a = 1) and (b = 6).

[x = \frac{-6}{2(1)}] [x = \frac{-6}{2}] [x = -3]

Therefore, the axis of symmetry is (x = -3).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.