Question

Which two points satisfy y = -x2 + 2x + 4 and x + y = 4?

Answer 1

(0,4) and (3,1)

Answer 2

\(\color{#000000}{ \displaystyle y = -x^2 + 2x + 4 }\)
\(\color{#000000}{ \displaystyle x+y=4\quad \quad \Longrightarrow \quad \quad y=-x+4 }\)

You want to know where these functions intersect so set them equal to each other, and solve for x. This will give you x-coordinates of the intersection (if any). Then using the x-coordinates, you can find the corresponding y-coordinates of the points.

Answer 3

\(\color{#000000}{ \displaystyle -x+4 = -x^2 + 2x + 4 }\)
\(\color{#000000}{ \displaystyle 0 = -x^2 + 3x }\)
\(\color{#000000}{ \displaystyle 0 = x(-x+3) }\)

\(\color{#000000}{ \displaystyle x=0 }\)
\(\color{#000000}{ \displaystyle -x+3=0 \quad \quad \Longrightarrow \quad \quad x=3 }\)

Answer 4

you proceed.