The power family y=axn, with nonzero constant a, includes exponents 0,1,2,3. For n=0, use the constant function y=a, including at x=0; no evaluation of 00 is needed. **Power** | **Shape for positive coefficient** n=0 | Horizontal line n=1 | Straight line through the origin n=2 | Upward-opening parabola, symmetric about the y-axis n=3 | Increasing cubic curve through the origin Example The sketches show y=x2 and y=x3. At x=-2, their values are 4 and -8, respectively. The square graph has equal outputs at opposite inputs; the cube graph has opposite outputs. Multiplying by a negative coefficient reverses every output sign, reflecting the graph in the horizontal axis. The graph of y=-x2 therefore opens downward; y=-x3 decreases from left to right.

The power family \(y=ax^n\), with nonzero constant \(a\), includes exponents \(0,1,2,3\). For \(n=0\), use the constant function \(y=a\), including at \(x=0\); no evaluation of \(0^0\) is needed.

The sketches show \(y=x^2\) and \(y=x^3\). At \(x=-2\), their values are \(4\) and \(-8\), respectively. The square graph has equal outputs at opposite inputs; the cube graph has opposite outputs.

Multiplying by a negative coefficient reverses every output sign, reflecting the graph in the horizontal axis. The graph of \(y=-x^2\) therefore opens downward; \(y=-x^3\) decreases from left to right.

Constant, linear, square and cube graphs

Constant, linear, square and cube graphs

Power	Shape for positive coefficient
\(n=0\)	Horizontal line
\(n=1\)	Straight line through the origin
\(n=2\)	Upward-opening parabola, symmetric about the y-axis
\(n=3\)	Increasing cubic curve through the origin