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

• Dec 15th 2009, 04:16 AM
Candy101
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)
• Dec 15th 2009, 05:16 AM
Stroodle
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.
• Dec 15th 2009, 05:24 AM
earboth
Quote:

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 $\displaystyle y = -4 \cdot |7| + 20 = -8$

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

$\displaystyle -4 |x+7| + 20 = 0$
• Dec 15th 2009, 05:42 AM
Candy101
ok so do i

making it |x+7|+24???
• Dec 15th 2009, 05:53 AM
Soroban
Helloo, Candy101!

Quote:

How would i sketch something like this?

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

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

                  |       *          |          *         *        |        *           *      |      *             *    |    *               *  |  *                 * | *     -------------*--------------                   |

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

    *                        | *       *                      *         *                  * |           *              *  |             *          *    |               *      *      |                 *  *        |   ---------------*-----------+------                 -7          |

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

                              |             *          *    |             *        *      |               *      *      |               *    *        |                 *  *        |                 * *          |       ------------*-----------+------                 -7          |

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

                              |                 -7          |       ------------*-----------+----                 * *          |                 *  *        |               *    *        |               *      *      |             *        *      |             *          *    |                               |

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

                          |                   *      |                 * *      |                 *  *    |               *    *    |               *      *  |       -------*---------*--+--------             *          * |           *            *|           *              *         *                |*         *                | *       *                  |  *                           |

You should be able to answer the questions now.