## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

The graph of $f(x)=ax^{2}$ is a parabola with $x=0$ as its axis of symmetry. Its vertex is the origin. For $a\gt 0$, the parabola opens upward. For $a\lt 0$, the parabola opens downward. If $|a|$ is greater than 1, the parabola is narrower than $y=x^{2}.$ If $|a|$ is between $0$ and 1, the parabola is wider than $y=x^{2}.$ The vertex of the graph of $f(x)=a(x-h)^{2}$ is $(h, 0)$ . --- $a=-\displaystyle \frac{1}{3}$, opens downward. The vertex is $(0,0)$. Make a table of function values and plot the points, and join with a smooth curve.