Question

Determine the equation of the graph with the coordinates of (4, -1)

O y = (x-4)2 - 1
O y=(x + 4)2 + 1
O y = (x + 4)2 - 1
O y = (x - 4)2 + 1

Answer 1

The required equation of the graph with the coordinates of (4, -1) will be:

• 
  `y=\left(x-4\right)^2-1`

The graph is also attached.

Explanation:

Given the coordinates (4, -1)

If we put the coordinate values (4, -1) in the given equations, we determine that only
`y=\left(x-4\right)^2-1` is the valid equation as it satisfies the given coordinate value.

For example, putting (4, -1) in the equation

`y=\left(x-4\right)^2-1`

`\left(-1\right)=\left(4-4\right)^2-1`

`-1=\left(0\right)^2-1`

`-1=0-1`

`-1=-1`

So, the equation
`y=\left(x-4\right)^2-1` is true for the coordinate values (4, -1).

Therefore, the required equation of the graph with the coordinates of (4, -1) will be:

• 
  `y=\left(x-4\right)^2-1`

Please check, the graph is also attached.