Respuesta :

Answer:

We are given a inequality as:

[tex]y\leq -x^2+2x[/tex]

  • We know that the graph of this inequality will be a solid parabola ( since the inequality is with equality sign) .
  • The parabola will be downward parabola ( Since for any general equation of parabola as y=ax^2+bx+c if a<0 then the parabola is downward and if a>0 then the parabola is upward)
  • Also the roots of the parabola are the points where y=0.

        (    The roots are:  -x(x-2)=0

          x=0 and x=2 are the roots of the parabola)

  • Also the region inside the parabola is shaded.

        (This could be checked by taking different points)

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MrRoyal

Inequalities are used to represent unequal expressions.

The solution to the inequality is: [tex]\mathbf{(x,y) \ge \{(0,0),(-2,-4)\}}[/tex]

The inequality is given as:

[tex]\mathbf{y \le - x^2 + 2x}[/tex]

The first step is to split the inequality as follows:

[tex]\mathbf{y \le - x^2}[/tex]

[tex]\mathbf{y \le 2x}[/tex]

Next, plot the graphs of the inequalities

i.e. the graphs of [tex]\mathbf{y \le - x^2}[/tex] and [tex]\mathbf{y \le 2x}[/tex] (see attachment for the graph)

Lastly, select the point or points of intersection of the graphs of [tex]\mathbf{y \le - x^2}[/tex] and [tex]\mathbf{y \le 2x}[/tex]

From the attached graph, the points of intersection of [tex]\mathbf{y \le - x^2}[/tex] and [tex]\mathbf{y \le 2x}[/tex] are:

[tex]\mathbf{(x,y) = \{(0,0),(-2,-4)\}}[/tex]

Hence, the solution to the inequality is:

[tex]\mathbf{(x,y) \ge \{(0,0),(-2,-4)\}}[/tex]

Read more about graphs of inequalities at:

https://brainly.com/question/15748955

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