We want to order the given quadratic functions from widest to narrowest graph.

f (x) = - 2 x^{2}, f (x) = - \frac{2}{3} x^{2}, and f (x) = - 4 x^{2}

First, we will draw the graphs of the three functions on the same coordinate plane. Then we can compare the graphs. To graph them, we will make a table of values for each function, including a variety of positive and negative inputs.

	$f (x) = - 2 x^{2}$		$f (x) = - \frac{2}{3} x^{2}$		$f (x) = - 4 x^{2}$
$x$	$- 2 x^{2}$	$(x, y)$	$- \frac{2}{3} x^{2}$	$(x, y)$	$- 4 x^{2}$	$(x, y)$
$- 2$	$- 2 (- 2)^{2}$	$(- 2, - 8)$	$- \frac{2}{3} (- 2)^{2}$	$(- 2, - \frac{8}{3})$	$- 4 (- 2)^{2}$	$(- 2, - 16)$
$- 1$	$- 2 (- 1)^{2}$	$(- 1, - 2)$	$- \frac{2}{3} (- 1)^{2}$	$(- 1, - \frac{2}{3})$	$- 4 (- 1)^{2}$	$(- 1, - 4)$
$0$	$- 2 (0)^{2}$	$(0, 0)$	$- \frac{2}{3} (0)^{2}$	$(0, 0)$	$- 4 (0)^{2}$	$(0, 0)$
$1$	$- 2 (1)^{2}$	$(1, - 2)$	$- \frac{2}{3} (1)^{2}$	$(1, - \frac{2}{3})$	$- 4 (1)^{2}$	$(1, - 4)$
$2$	$- 2 (2)^{2}$	$(2, - 8)$	$- \frac{2}{3} (2)^{2}$	$(2, - \frac{8}{3})$	$- 4 (2)^{2}$	$(2, - 16)$

Now, let's draw the parabolas by plotting and connecting the obtained points.

Looking at the graphs, we can order the functions from widest to narrowest.

f (x) = - \frac{2}{3} x^{2}, f (x) = - 2 x^{2}, f (x) = - 4 x^{2}

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