Respuesta :

sqdancefan

Answer:

  2 solutions

Step-by-step explanation:

A graph shows the line crosses the parabola in two places, (-1, 4) and (2, -2). There are two solutions.

__

If you want to solve this algebraically, you can equation the expressions for y and solve the resulting quadratic.

  y = y

  x^2 -3x = -2x +2

  x^2 -x -2 = 0 . . . . . . put in standard form

To find the number of solutions, you can look at the discriminant. For quadratic ax²+bx+c, the discriminant is ...

  d = b² -4ac

For the quadratic in this problem, the discriminant is ...

  d = (-1)^2 -4(1)(-2) = 1 +8 = 9

This is a positive number, meaning that there are two distinct real solutions.

_____

Additional comment

The discriminant of a quadratic can tell you the number of solutions, and whether they are real or complex:

  • d < 0 . . . two complex solutions
  • d = 0 . . . one real solution
  • d > 0 . . . two real solutions
Ver imagen sqdancefan
temdan2001

The roots of the system of equation are 2 and -1. Therefore, the system of equations have two solutions

Given that y=−2x+2 and y=x^2−3x

Equate the two equations

-2x + 2 = x^2 − 3x

collect the like terms

x^2 − 3x + 2x - 2 = 0

x^2 − x - 2

Factorize the quadratic equation above

x^2 + x − 2x - 2 = 0

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

x - 2 = 0

x = 2

or

x + 1 = 0

x = -1

Therefore, the system of equations have two solutions

Learn more about Equation here : https://brainly.com/question/13763238

Otras preguntas