Question

Please help me with this!!

Answer 1

Step-by-step 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.