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

y = - \frac{1}{2} x^{2}, y = 5 x^{2}, and y = - \frac{1}{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.

	$y = - \frac{1}{2} x^{2}$		$y = 5 x^{2}$		$y = - \frac{1}{4} x^{2}$
$x$	$- \frac{1}{2} x^{2}$	$(x, y)$	$5 x^{2}$	$(x, y)$	$- \frac{1}{4} x^{2}$	$(x, y)$
$- 2$	$- \frac{1}{2} (- 2)^{2}$	$(- 2, - 2)$	$5 (- 2)^{2}$	$(- 2, 20)$	$- \frac{1}{4} (- 2)^{2}$	$(- 2, - 1)$
$- 1$	$- \frac{1}{2} (- 1)^{2}$	$(- 1, - \frac{1}{2})$	$5 (- 1)^{2}$	$(- 1, 5)$	$- \frac{1}{4} (- 1)^{2}$	$(- 1, - \frac{1}{4})$
$0$	$- \frac{1}{2} (0)^{2}$	$(0, 0)$	$5 (0)^{2}$	$(0, 0)$	$- \frac{1}{4} (0)^{2}$	$(0, 0)$
$1$	$- \frac{1}{2} (1)^{2}$	$(1, - \frac{1}{2})$	$5 (1)^{2}$	$(1, 5)$	$- \frac{1}{4} (1)^{2}$	$(1, - \frac{1}{4})$
$2$	$- \frac{1}{2} (2)^{2}$	$(2, - 2)$	$5 (2)^{2}$	$(2, 20)$	$- \frac{1}{4} (2)^{2}$	$(2, - 1)$

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.

y = - \frac{1}{4} x^{2}, y = - \frac{1}{2} x^{2}, y = 5 x^{2}

Exercise

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