Example 1
Completion requirements
| Example 1 |
Multimedia |
Graph the inequality \(y < 3x^2 -12x + 13\).
Start by graphing the corresponding function, \(y = 3x^2 - 12x + 13\). The inequality is strict, so graph the boundary with a dashed curve.
A test point can be used to determine which region to shade. Here, \((0,0)\) is used.
The point \((0,0)\) satisfies the inequality, so it and all other points on that side of the boundary are solutions. Shade the regions that includes the test point.
A test point can be used to determine which region to shade. Here, \((0,0)\) is used.
| Left Side | Right Side |
|---|---|
|
\[\begin{array}{r}
y \\ 0 \end{array}\] |
\[\begin{array}{l}
3x^2 - 12x + 13\\ 3(0)^2 - 12(0) + 13 \\ 13 \end{array}\] |
| \(\hspace{25pt}\)LS \(\lt\) RS | |
The point \((0,0)\) satisfies the inequality, so it and all other points on that side of the boundary are solutions. Shade the regions that includes the test point.