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Complete the function table for the given domain and plot the points on the graph. f(x)=(x-5)^2+1

User Idik
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1 Answer

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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).

User Digitig
by
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