Answer:
Vertex: [tex]V(x,y) =(5, -16)[/tex]
Axis of symmetry: [tex]x = 5[/tex]
Max/Min value of the function: The minimum value of the curve is -16
Step-by-step explanation:
The correct statement is now described:
Identify the vertex, axis of symmetry and the max/min value of the function.
[tex]y = (x-5)^{2}-16[/tex]
Vertex
Based on the definition of the standard form of the equation of the parabola with a vertical axis of symmetry we can find where the vertex is:
[tex]y - k = C\cdot (x-h)^{2}[/tex] (1)
Where:
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex, dimensionless.
[tex]C[/tex] - Constant, dimensionless.
[tex]x[/tex], [tex]y[/tex] - Independent and independent variables, dimensionless.
The standard form of the given equation is:
[tex]y+16 = 1\cdot (x-5)^{2}[/tex]
Then, we notice that the vertex of parabola is located at [tex]V(x,y) =(5, -16)[/tex].
Axis of symmetry
In this case, the axis of symmetry corresponds to a vertical line that passes through the vertex. Therefore, the axis of symmetry is represented by [tex]x = 5[/tex].
Max/Min value of the function
Given that the constant ([tex]C[/tex]) is greater than zero, it means that given parabola contains an absolute minimum represented by the vertex. Then, the minimum value of the curve is -16.
