Pregunta
Graph the solution set of the following system of inequalities.
Ask by Lynch Wyatt. in the United States
Dec 06,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The solution set is the region where the line
and the parabola
overlap.
Solución

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Como
Bonus Knowledge
To graph the solution set for the system of inequalities, let’s break it down step-by-step:
First, rewrite the inequalities for easier graphing:
-
Inequality 1:
can be rearranged to or . This is a straight line with a y-intercept at and a slope of . Since it is a “less than or equal to” inequality, the line will be solid. -
Inequality 2:
describes a parabola opening upwards with vertex at . For this inequality, the region will be shaded above the parabola, indicating that this is a “greater than or equal to” situation, so the line of the parabola is also solid.
To graph these inequalities:
-
Start by drawing the line for
. Plot the y-intercept (0, 2) and use the slope to find another point (e.g., for , ). Draw a solid line through these points and shade below it. -
Next, sketch the parabola
. Mark the vertex at (0, -3) and a few additional points, like (-1, -2) and (1, -2). Then draw the parabola, making sure to shade the area above it.
Finally, the solution set for the system of inequalities is where the shaded regions overlap. This area represents all the points
that satisfy both inequalities.

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