Question

Trey graphs the equations y = –x2 + 2x + 3 and y = x2 – 2x + 3 to solve the equation –x2 + 2x + 3 = x2 – 2x + 3. His graph is shown below.

mc011-1.jpg

What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?

Answer 1

all you have to do is go on desmos calculator and type those two equations in the two point where the graph meets are the solutions to this problems (0,3) and (2,3)

Answer 2

The solution of the equation
`-x^2+2x+3=x^2-2x+3` are the x-coordinates of common points on the graphs of the function
`y=-x^2+2x+3` and
`y=x^2-2x+3.`

As you can see from the attached diagram these graphs intersect at points (0,3) and (2,3), then the solutions of the previous equation are x=0 and x=2.

Answer: x=0, x=2.