How do you graph the function $y=-1/2x^2-2x$ and identify the domain and range?

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Answer 1 · 2017-01-29T22:32:03

Draw an upside parabola that goes through the origin and the point $(-4, 0)$ and has a maximum at $y=2$

Step 1. Find the roots of the parabola by letting $y=0$ and solve for $x$ .

$-1/2 x^2-2x=0$
$x(-1/2 x - 2)=0$

When $x=0$ , then $y=0$ . That's at the origin $(0,0)$

Also, if we let

$-1/2 x - 2 = 0$
$-2*(-1/2 x - 2) = -2*0$
$x+4=0$
$x=-4$ .

So our two roots are $(0,0)$ and $(-4,0)$ .

Step 2. Find the maximum $y$ -value by using the formula: $x_"max"=-b/(2a)$ , were $b=-2$ and $a=-1/2$
$x_"max"=-(-2)/(2*(-1/2))=-2$

Plugging this value of $x_"max"=-2$ into the original formula, gives the value of $y$ at that $x_"max"$ value. So,

$y=-1/2(-2)^2-2(-2)=-2+4=2$

That is, there is a maximum of the parabola at $(-2,2)$ . Now we can draw the graph:

graph{-1/2x^2-2x [-11.91, 8.09, -5.2, 4.8]}

How do you graph the function y=-1/2x^2-2xy=-1/2x^2-2x and identify the domain and range?