Answer:
The vertex of the parabola will be at (5, 1).
Explanation:
To complete the function table for the given function f(x) = (x-5)^2 + 1, we need to choose some values for x and evaluate the function to find the corresponding y-values. Here's how we can do that:
Let's choose a few values for x and calculate the corresponding y-values:
For x = 0:
f(0) = (0 - 5)^2 + 1
= (-5)^2 + 1
= 25 + 1
= 26
So, when x = 0, y = 26.
For x = 1:
f(1) = (1 - 5)^2 + 1
= (-4)^2 + 1
= 16 + 1
= 17
So, when x = 1, y = 17.
For x = 5:
f(5) = (5 - 5)^2 + 1
= (0)^2 + 1
= 0 + 1
= 1
So, when x = 5, y = 1.
For x = 10:
f(10) = (10 - 5)^2 + 1
= (5)^2 + 1
= 25 + 1
= 26
So, when x = 10, y = 26.
Now, let's plot these points on the graph. The x-values will be the points along the x-axis, and the y-values will be the points along the y-axis:
(x, y) = (0, 26)
(x, y) = (1, 17)
(x, y) = (5, 1)
(x, y) = (10, 26)
Plotting these points on the graph, we can see the shape of the function. The graph will be a U-shaped curve opening upwards. The vertex of the parabola will be at (5, 1).