Exercise 18 Page 550

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

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

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.