coolgirlaxline
contestada

Find the solution(s) of the system of equations:
y = –x2 + 4x + 5
y = x2 + 2x + 1

a. (–1,2) and (2,17)
b. (1,0) and (–2,9)
c. (1,4) and (2,9)
d. (–1,0) and (2,9)

Respuesta :

mattwisey26
The correct solution is D or (-1,0) and (2,9).

The easiest way to find the solutions is to graph the equations then observe the coordinate intersections of each graph :)
Ver imagen mattwisey26
abidemiokin

The solution to the equation are (2, 9) and (-1, 0)

Given the functions as shown below:

  • y = –x2 + 4x + 5
  • y = x2 + 2x + 1

Equating both equations will give;

–x^2 + 4x + 5 = x^2 + 2x + 1

Collect the like terms to have:

–x^2 + 4x + 5 –x^2 - 2x - 1 = 0

-2x^2 + 2x + 4= 0\

2x^2 - 2x - 4  = 0

x^2 - x - 2 =0

Factorize to have:

x^2 - x - 2 =0

x^2 - 2x + x - 2 = 0

x(x-2)+1(x-2) = 0

x = 2 and -1

If x = 2

y = 2^2 + 2(2) + 1

y = 9

If x  = -1

y = (-1)^2 + 2(-1) + 1

y = 1 - 2 + 1

y = 0

Hence the solution to the equation are (2, 9) and (-1, 0)

Learn more on equations here: https://brainly.com/question/16863577