Answer
$\color{blue}{[1, 3]}$
Refer to the image below for the graph.
Work Step by Step
To solve the given inequality graphically, perform the following steps:
(1) Let each side of the equation represent a function then graph each function on the same coordinate plane.
Graph $y=4x-3$ (the blue graph) and $y=x^2$ (the red graph).
(refer to the attached image in the answer part above for the graph)
(2) Identify the region/s where the blue graph has a greater value than the red graph. The interval/s that cover these regions make up the solution set of the given inequality.
Note that the blue graph is higher than the red graph from $x=1$ to $x=3$.
This means that the value of $4x-3$ is greater than or equal to the value of $x^2$ in the interval $(1. 3)$.
Since the inequality involves $\ge$, then the endpoints $1$ and $3$ are part of the solution set.
Therefore, the solution set is:
$\color{blue}{[1, 3]}$
