# Math Help - how would i even begin to solve this..plzz help

1. ## how would i even begin to solve this..plzz help

how would i sketch something like this?

y= -4 | x+7 | + 20 and indicate its vertex and all intercepts

i am thinking that i should add 4 to both sides making it |x+7|+24??

i don't know how to solve this...(this is so hopeless for me)

2. One way to sketch it is to first sketch the graph of y=x+7, remembering to reflect the part of the graph that is below the x-axis. Then apply the dilation of -4 (multiply each value by -4, this will reflect the entire graph in the x-axis) After this you can then translate the graph 24 units in the positive direction of the y-axis.

3. Originally Posted by Candy101
how would i sketch something like this?

y= -4 | x+7 | + 20 and indicate its vertex and all intercepts

i am thinking that i should add 4 to both sides making it |x+7|+24??

i don't know how to solve this...(this is so hopeless for me)
1. The smallest value an absolute value can get is zero. This happens here at x = -7. Then the y-coordinate is 20. This is your vertex V(-7, 20).

2. The y-intercept is at x = 0; then $y = -4 \cdot |7| + 20 = -8$

3. The x-intercepts are at y = 0. Thus you have to solve for x:

$-4 |x+7| + 20 = 0$

4. ok so do i

add 4

making it |x+7|+24???

5. Helloo, Candy101!

How would i sketch something like this?

$y \:=\: -4|x+7| + 20$ . and indicate its vertex and all intercepts

We are expected to know the graph of: $y \:=\:|x|$
Code:
                  |
*           |           *
*         |         *
*       |       *
*     |     *
*   |   *
* | *
-------------*--------------
|

The graph of: . $y \:=\:|x+7|$ .is the previous graph moved 7 units to the left.
Code:
    *                         | *
*                       *
*                   * |
*               *   |
*           *     |
*       *       |
*   *         |
---------------*-----------+------
-7           |

The graph of: . $y \:=\:4|x+7|$ .is the previous graph only "steeper".
Code:
                              |
*           *     |
*         *      |
*       *       |
*     *        |
*   *         |
* *          |
------------*-----------+------
-7           |

The graph of: $y \:=\:-4|x+7|$ . is the previous graph reflected over the x-axis.
Code:
                              |
-7           |
------------*-----------+----
* *          |
*   *         |
*     *        |
*       *       |
*         *      |
*           *     |
|

The graph of: $y \:=\:-4|x+7| + 20$ .is the previous graph raised 20 units.
Code:
                          |
*       |
* *      |
*   *     |
*     *    |
*       *   |
-------*---------*--+--------
*           * |
*             *|
*               *
*                |*
*                 | *
*                  |  *
|

You should be able to answer the questions now.