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

–1 and 3
0 and 2
0
3

Answer 1

0 and 2 are both solutions

Answer 2

Answer:

0 and 2.

Step-by-step explanation:

Given equations,

$y=-x^2+2x+3-----(1)$

$y=x^2-2x+3----(2)$

Equation (1) is a downward parabola,

Vertex = (1, 4),

y-intercept = (0, 3),

No x-intercept,

While, equation (2) is an upward parabola,

Vertex = (1, 2)

y-intercept = (0, 3)

x -intercept = (3, 0) and (-1, 0)

By the above explanation we can form the graph of the equations (1) and (2), ( shown below )

In the graph equation (1) and (2) are intersecting at (0, 3) and (2, 0),

Hence, the solution of $-x^2 + 2x + 3 = x^2 - 2x + 3$ would be 0 and 2 ( x-coordinates of the intersected points )

Second option is correct.