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:SAMPLE QUESTION The absolute value function is symmetric with its vertex on the line of symmetry. Because the points (–6, –2) and  (0, –2) have the same output, the points are the same distance from the line of symmetry. Midway between –6 and 0 is the value of –3. Therefore, the vertex must have an x-coordinate of –3, which is the value of h. This would translate the graph of the parent function 3 units to the left.

Step-by-step explanation:

Answer 2

h = -3

What is a parent function?

A parent function is the simplest function that still satisfies the definition of a certain type of function.

f(x) = |x – h| + k

points (–6, –2) and (0, –2)

=> - 2 = | - 6 - h |  + k    

    -2 =  |  - h |  + k

Hence,

| - 6 - h | = | - h |

There are two possible cases

- 6 - h = - h       or   -6 - h =  h

=> -6 = 0          or    h = - 3

not possible            Hence h = - 3

-2 =  |  - h |  + k

=> - 2 = | -(-3)| + k

=>  k = - 5

Parent function  f(x) = | x |

f(x) = |x – h| + k

f(x) = | x  -(- 3) | - 5

Hence Shifted horizontally 3 units on the left

and  5 units vertically down

Graph has vertex at (-3 , - 5)      

the value of h is - 3

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