Respuesta :

giantninja908

Answer:

(-3,4)

Step-by-step explanation:

The axis of symmetry, or X coordinate for a parabolic function is [tex]\frac{-b}{2a}[/tex]

By plugging in 6 for b, and 1 for a, you have -3.

By then plugging back into the function you can get the Y coordinate of the vertex.

[tex]f(x)=(-3)^{2}+6(-3)+13[/tex]

Or 4.

The answer is (-3,4)

kudzordzifrancis

ANSWER

(-3, 4)

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 6x + 13[/tex]

We complete the square to obtain the vertex form:

We add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} + 6x + {3}^{2} + 13 - {3}^{2} [/tex]

The first three terms form a perfect square trinomial.

[tex]f(x) = {(x + 3)}^{2} + 13 - 9[/tex]

[tex]f(x) = {(x + 3)}^{2} + 4[/tex]

Comparing this to the vertex form;

[tex]f(x) = {(x - h)}^{2} + k[/tex]

h=-3 and k=4

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