Answer:
The vertex is located at (3,5)
The axis of symmetry is x = 3
The plot is in the image attached
Step-by-step explanation:
First we need to find the vertex of the quadratic function. We can find the x-coordinate of the vertex using the formula:
x_v = -b / 2a
Where 'a' and 'b' are coefficients of the quadratic equation in the model:
ax^2 + bx + c = 0
Then we need to expand the terms of f(x):
f(x) = (x-3)^2 + 5
f(x) = x^2 - 6x + 9 + 5
f(x) = x^2 - 6x + 14
So we have a = 1 and b = -6
Then the x-coordinate of the vertex is:
x_v = 6 / 2 = 3
We can use this value in f(x) to find the y-coordinate of the vertex:
f(x_v) = 3^2 - 6*3 + 14 = 5
So the vertex is located at (3,5)
The axis of symmetry is the vertical line traced in the vertex, so it is x = 3
The plot is in the image attached. The circle at (3,5) is the vertex, and the blue line is the axis of symmetry.
