Question

Graph the function $y=\frac{1}{2}{x}^2+x+\frac{3}{2}$.

Short answer

The graph of the function $y=\frac{1}{2}{x}^2+x+\frac{3}{2}$ is shown below.

Step-by-step solution

Step 1. Write down the given information.

The given function is $y=\frac{1}{2}{x}^2+x+\frac{3}{2}$.

Step 2. Construct the graph of the given function.

The graph of the function $y=\frac{1}{2}{x}^2+x+\frac{3}{2}$ is shown below.

Step 3. Interpretation from the graph.

From the graph it can be interpreted that the graph does not cut x-axis at any point. Hence it will have no real solutions.