Question

A two-variable inequality is shown in the graph.

Answer 1

The point which is not included in the solution set for the inequality of the two-variable inequality shown in the graph is (-1,3).

How to graph the inequality?

Inequality of a graph is represented with the greater then(<), less then(>) or with the other inequity signs. The inequality line on the graph is represented with the dotted lines.

A two-variable inequality is shown in the graph. It is a parabola.  The vertex form of parabola is the equation form of quadratic equation which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.

The standard equation of the vertex form of parabola is given as,

$y=a(x-h)^2+k$

Here, (h, k) is the vertex point. In the graph, vertex points are (1,2). Thus, the equation become,

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

By the point of graph (0,3), find the value of a,

$3=a(0-1)^2+2\\3=a+2\\a=3-2\\a=1$

Thus, the equation become,

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

The graph of this line is attached below. In this graph only point (-1,3), does not fall hence, does not satisfy the equation.

Thus, the point which is not included in the solution set for the inequality of the two-variable inequality shown in the graph is (-1,3).

Learn more about the graph of the inequality here;

brainly.com/question/62792

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