Question

Which two points satisfy y = -x^2 + 2x + 4 and x + y = 4?

Answer 1

x^2 + y -2x = x + y x^2 - 3x = 0 x (x - 3) = 0 x = 0 or x = 3

Answer 2

The solution to the given equation is at point (0,4) and (3,1)

Explanation:

Given : Two equations

`y = -x^2 + 2x + 4` and
`x + y = 4`

To find : Which two points satisfy the given equations?

Solution :

Let,
`y=-x^2 + 2x + 4` (equation 1)

and
`x + y = 4` (equation 2)

Now, We solve these equation with the help of graph.

We plot these two equations.

The graph of
`y=-x^2 + 2x + 4` is shown with green line.

The graph of
`x + y = 4` is shown with violet line.

The solution to this system will be their intersection point.

The intersection points of these graph are (0,4) and (3,1)

Refer the attached graph below.

Therefore, The solution to the given equation is at point (0,4) and (3,1)