Explain how to graph the inequality \( y < x^{2} + 3x - 4 \) on a coordinate plane.

To graph the inequality \( y < x^{2} + 3x - 4 \), start by rewriting the equation as \( y = x^{2} + 3x - 4 \), which represents a parabola. First, find the vertex and intercepts of the parabola; the vertex can be located using the formula \( x = -\frac{b}{2a} \). For this equation, it’s at \( x = -\frac{3}{2} \). Plot this vertex and the curve on the graph, then draw the parabola as a dashed line since the inequality is strict (not including equals). Finally, shade the area below the curve to represent all the points where \( y < x^2 + 3x - 4 \). To avoid confusion while shading, remember that the region below the parabola includes all points with a lower \( y \)-value than the curve at any given \( x \). A vital tip is to test a point that you know is not on the boundary line (like \( (0, 0) \)). If substituting this into the inequality yields a true statement, it indicates that region is correctly shaded, while the areas above the curve should remain unshaded.