Question

The graph of f(x) = |x-h| + k contains the points (-6, -2)
and (0, -2). The graph has a vertex at (h,-5). Describe
how to find the value of h. Then, explain how this value
translates the graph of the parent function.

Answer 1

Answer:

(-3, -5)

How to do it:

To find the value of h, you must find the midway point between the 2 x coordinates given. With the two given coordinates, (-6, -2,) and (0, -2,) the midway point would be -3. Because the distance between -3 and -6 or 0 is 3 units, and the coordinates given started at -2, the y coordinate would be -5. In conclusion, the answer would be (-3, -5.)

Disclaimer: my y coordinate may not be correct, however the x is all that the question is asking for, and I've already completed it. The x is 100% correct.

Answer 2

The vertex of a graph is the maximum or minimum point on the graph.

• The value of h is -3
• The parent function is shifted left by 3 units, and shifted down by 5 units.

The given parameters are:

$\mathbf{(x_1,y_1) = (-6,-2)}$

$\mathbf{(x_2,y_2) = (0,-2)}$

$\mathbf{(h,k) = (h,-5)}$

The general absolute function is:

$\mathbf{y = |x - h| + k}$

Substitute $\mathbf{(x_1,y_1) = (-6,-2)}$ and $\mathbf{(h,k) = (h,-5)}$ in $\mathbf{y = |x - h| + k}$

$\mathbf{-2 = |-6 - h| -5}$

Add 5 to both sides

$\mathbf{3 = |-6 - h|}$

Rewrite as:

$\mathbf{|-6 - h| = 3}$

Remove absolute bracket

$\mathbf{-6 - h = 3}$ or $\mathbf{-6 - h = -3}$

Add 6 to both sides

$\mathbf{-h = 9}$ or $\mathbf{-h = 3}$

$\mathbf{h = -9}$ or $\mathbf{h = -3}$

From the given parameters, the graph cross the x-axis at x = -6 and x = 0

So, the value of h must be between these x-values

Hence, the value of h is -3

$\mathbf{y = |x - h| + k}$ becomes

$\mathbf{y = |x + 3| -5 }$

This means that, the parent function is shifted left by 3 units, and shifted down by 5 units.

Read more about transformation of absolute functions at:

https://brainly.com/question/13202169