How to graph a parabola #f(x) = 2/3x^2 - 5#?

To graph the parabola (f(x) = \frac{2}{3}x^2 - 5), you can follow these steps:

1. Identify the vertex of the parabola using the formula (h = -\frac{b}{2a}), where (a = \frac{2}{3}) and (b = 0) (since there is no linear term).
2. Substitute the value of (h) back into the equation to find the (y)-coordinate of the vertex.
3. Plot the vertex on the coordinate plane.
4. Determine the direction of the parabola by observing the sign of the coefficient of (x^2). Since it's positive ((\frac{2}{3})), the parabola opens upwards.
5. Choose additional points on either side of the vertex and plot them on the graph.
6. Draw a smooth curve passing through the plotted points to represent the parabola.

If you need to determine additional points, you can choose values of (x) and calculate the corresponding (y) values using the equation (f(x) = \frac{2}{3}x^2 - 5).