Question

Please help me with this!!

Answer 1

Explanation:

To find the y-coordinate points we need to evaluate the function for all the
`x` values in the table. In other words, we need to replace
`x` with each value in our given function and simplify.

- For x = 0

`f(x)=(x-2)^2-5`

`f(0)=(0-2)^2-5`

`f(0)=(-2)^2-5`

`f(0)=4-5`

`f(x)=-1`

Since
`x=0` and
`y=-1`, our first point is (0, -1)

- For x = 1

`f(x)=(x-2)^2-5`

`f(1)=(1-2)^2-5`

`f(1)=(-1)^2-5`

`f(1)=1-5`

`f(x)=-4`

Our second point is (1, -4)

- For x = 2

`f(x)=(x-2)^2-5`

`f(2)=(2-2)^2-5`

`f(2)=(0)^2-5`

`f(x)=-5`

Our third point is (2, -5)

- For x = 3

`f(x)=(x-2)^2-5`

`f(3)=(3-2)^2-5`

`f(3)=(1)^2-5`

`f(3)=1-5`

`f(x)=-4`

Our fourth point is (3, -4)

- For x = 4

`f(x)=(x-2)^2-5`

`f(4)=(4-2)^2-5`

`f(4)=(2)^2-5`

`f(4)=4-5`

`f(x)=-1`

Our fifth point is (4, -1)

Now we just need to plot each point in our coordinate plane and join them with the parabola as you can see in the attached picture.