Respuesta :
The vertex of the given quadratic function is (-3, 0).
What is vertex form of a quadratic equation?
The vertex form of a quadratic equation or function is [tex]f(x)=a(x-h)^{2} +k[/tex].
Where,
(h, k ) is the vertex
And, a is constant.
According to the given question
We have a quadratic function
[tex]f(x) = x^{2} + 6x + 9[/tex]
The above function can be written as
[tex]f(x) = x^{2} +2(3x) +9[/tex]
⇒[tex]f(x) = x^{2} + 2(3x) + (3^{2}) -(3)^{2} + 9[/tex]
⇒[tex]f(x) = (x+3)^{2} -9+9[/tex]
⇒[tex]f(x) = (x+3)^{2} + 0[/tex]
Comparing the above equation with the standard vertex form of quadratic function we get
h = -3 and k = 0
Hence, the vertex of the given quadratic function is (-3, 0).
Thus, option A is correct.
Find out more information about vertex form of a quadratic equation here:
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