Find the vertex of the parabola that represents the function f left parenthesis x right parenthesis equals left parenthesis x minus 5 right parenthesis squared plus 9.
(1 point)
Responses
left parenthesis 5 comma 9 right parenthesis
Image with alt text: left parenthesis 5 comma 9 right parenthesis
left parenthesis 0 comma 0 right parenthesis
Image with alt text: left parenthesis 0 comma 0 right parenthesis
left parenthesis negative 5 comma 9 right parenthesis
Image with alt text: left parenthesis negative 5 comma 9 right parenthesis
left parenthesis negative 5 comma negative 9 right parenthesis
Image with alt text: left parenthesis negative 5 comma negative 9 right parenthesis
The vertex form of a parabola is given by f(x) = (x - h)^2 + k, where (h, k) represents the vertex of the parabola.
In this case, f(x) = (x - 5)^2 + 9.
Comparing this with the vertex form, we can see that the vertex is located at (h, k) = (5, 9).
Therefore, the correct response is:
(5, 9)
To find the vertex of the parabola represented by the function f(x) = (x - 5)^2 + 9, we can use the formula:
Vertex = (h, k)
where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
In this case, the equation is already in vertex form, so we can easily identify the vertex.
Comparing the given equation with the vertex form equation:
f(x) = (x - h)^2 + k
we can see that h = 5 and k = 9.
Therefore, the vertex of the parabola is (5, 9).