Are you ready to delve into the fascinating world of mathematical inequalities? Brace yourself as we embark on a journey to unravel the secrets of solving the inequality graph for 2y > 2x². In this intriguing exploration, we will untangle the intricacies of this particular inequality, analyzing its properties and understanding how it translates into a visual representation on the Cartesian plane. Prepare to witness the power of mathematical reasoning as we overcome challenges and unlock solutions in our quest to conquer this exciting mathematical puzzle. So grab your pen and paper, fasten your seatbelt, and get ready to dive deep into the captivating world of inequality graphs!

When it comes to solving inequalities, one common method is to graph the inequality and determine the solution region. In this article, we will explore how to graph the inequality 2y > 2x² and find its solution.

To begin, let’s first understand what this inequality represents. The equation 2y > 2x² can also be written as y > x². It describes a region in the coordinate plane where y is greater than x squared. Graphing this inequality allows us to visualize the area that satisfies this condition.

To graph the inequality, we’ll start by creating a table of values and then plot these points on a coordinate plane. Let’s choose some x-values and find their corresponding y-values using the equation y = x².

Let’s take x = -2, -1, 0, 1, and 2 as our example values. Substituting these into the equation gives us:

For x = -2: y = (-2)² = 4

For x = -1: y = (-1)² = 1

For x = 0: y = (0)² = 0

For x = 1: y = (1)² = 1

For x = 2: y = (2)²=4

Now that we have our pairs of values (x, y), we can plot them on a graph. The points are (-2,4), (-1,1), (0,0), (1,1), and (2,4).

Next, we draw a smooth curve passing through these points. Since our inequality is greater than, we need a dashed line instead of a solid one to indicate that the boundary is not included in the solution.

Now that we have our graph plotted with its dashed line, we need to determine which side of the boundary satisfies the inequality y > x². We can select a test point on either side of the curve and substitute its coordinates into the inequality.

Let’s take the point (0,1) as a test point. Substituting these values into our inequality, we have:

2(1) > 2(0)²

2 > 0

Since 2 is indeed greater than 0, this means that all points on this side of the curve satisfy the inequality.

To summarize, when solving the inequality 2y > 2x² or y > x², we graphed it by creating a table of values, plotting points on a coordinate plane, and drawing a dashed line through those points. We then determined which side of the boundary satisfies the inequality by using a test point. In this case, any point on the side above our dashed curve satisfies the condition y > x².

Graphing inequalities helps us visualize solution regions and better understand their mathematical representations. It is an effective method for solving and analyzing various types of inequalities.

Remember to always double-check your work and pay attention to whether your inequality is inclusive or exclusive when graphing and interpreting solutions.