Question

graph the function $y = -2|x + 5| - 5$ using the given table of values and following the instructions below.

$x$	$y$
$-9$	$-13$
$-8$	$-11$
$-7$	$-9$
$-6$	$-7$
$-5$	$-5$
$-4$	$-7$

$x$	$y$
$-2$	$-11$
$-1$	$-13$
$0$	$-15$
$1$	$-17$
$2$	$-19$
$3$	$-21$

$x$	$y$
$5$	$-25$
$6$	$-27$
$7$	$-29$
$8$	$-31$
$9$	$-33$
$10$	$-35$

done plotting points

plot at least five points from the table of values on the axes below. click a point to delete it.

Explanation:

Step1: Recall the function

The function is \( y = -2|x + 5| - 5 \). This is an absolute - value function. The general form of an absolute - value function is \( y=a|x - h|+k \), where \((h,k)\) is the vertex of the V - shaped graph. For our function \( y=-2|x + 5|-5=-2|x-(-5)|+(-5) \), the vertex is at \((-5,-5)\).

Step2: Select points to plot

We can choose points from the given tables. Let's pick the following points:

• When \( x=-5 \), \( y=-5 \) (this is the vertex).
• When \( x=-6 \), substitute \( x = - 6\) into the function: \( y=-2|-6 + 5|-5=-2|-1|-5=-2\times1-5=-7 \) (matches the table).
• When \( x=-4 \), substitute \( x=-4\) into the function: \( y=-2|-4 + 5|-5=-2|1|-5=-2 - 5=-7 \) (matches the table).
• When \( x=-7 \), substitute \( x=-7\) into the function: \( y=-2|-7 + 5|-5=-2|-2|-5=-4 - 5=-9 \) (matches the table).
• When \( x=-3 \), substitute \( x=-3\) into the function: \( y=-2|-3 + 5|-5=-2|2|-5=-4 - 5=-9 \) (matches the table).

To plot the points:

1. Locate the point \((-5,-5)\) on the coordinate plane (the vertex, where the graph changes direction).
2. Locate \((-6,-7)\): move 6 units to the left of the origin on the x - axis and 7 units down on the y - axis.
3. Locate \((-4,-7)\): move 4 units to the left of the origin on the x - axis and 7 units down on the y - axis.
4. Locate \((-7,-9)\): move 7 units to the left of the origin on the x - axis and 9 units down on the y - axis.
5. Locate \((-3,-9)\): move 3 units to the left of the origin on the x - axis and 9 units down on the y - axis.

After plotting these points, we can see that the graph is a downward - opening V - shape (because \( a=-2<0 \)) with the vertex at \((-5,-5)\) and symmetric about the vertical line \( x=-5 \).

Answer:

To graph the function \( y = - 2|x + 5|-5\), plot the points (at least five) such as \((-5,-5)\), \((-6,-7)\), \((-4,-7)\), \((-7,-9)\), \((-3,-9)\) on the coordinate plane. The graph is a downward - opening V - shaped graph with vertex at \((-5,-5)\) and symmetric about \( x=-5 \).