Draw a sketch of the graph of the region in which the points satisfy the given system of inequal

step 1 Okay, so here we have first the graph of y is greater than x squared. So we just make the graph

Draw a sketch of the graph of the region in which the points...

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Key Concepts

Quadratic Function

A quadratic function is a polynomial function of degree two, typically represented as y = ax² + bx + c. Its graph is a parabola, which can open upward or downward depending on the coefficient of x². In the context of inequalities, the quadratic function defines a curved boundary that splits the plane into two regions, helping to establish which points satisfy the inequality.

Linear Function

A linear function is a first-degree function, usually written in the form y = mx + b, representing a straight line in the coordinate plane. When used in inequalities, the line acts as a boundary that divides the plane into two halves, with one side satisfying the inequality condition.

Graphing Inequalities

Graphing inequalities involves drawing the boundary given by the equality and then shading the region of the graph that satisfies the inequality. This process requires determining whether the boundary itself is included (solid line) or not (dashed line) and identifying the correct side of the boundary to shade.

Intersection of Regions

When dealing with systems of inequalities, the solution set is the intersection, or overlap, of the regions defined by each inequality. This concept is crucial because only the points that belong to all the individual regions will satisfy the entire system of inequalities.

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