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34kurt
2 years ago
11

Determine the Vertex of the following absolute value function.

Mathematics
1 answer:
prisoha [69]2 years ago
6 0

Answer:

vertex = (-4, 5)

Step-by-step explanation:

In general, the graph of the absolute value function f(x) = a|x - h| + k will have its lowest value when f(x) = k  (or highest value for f(x) = -a|x - h| + k).  The lowest/highest value is the vertex (turning point).

Therefore, from inspection of the equation we can say that the y-coordinate of the vertex is 5.

Set the equation to 5 and then solve for x:

⇒ 5 = 1/2 |-X – 4| + 5

⇒ 1/2 |-X – 4| = 0

⇒ |-X – 4| = 0

Therefore, (-X - 4) = 0  and -(-X - 4) = 0

⇒ X = -4 (for both)

So the vertex is (-4, 5)

<u>Translations</u>

Absolute value parent function:  f(x) = | -x |

Horizontal translation left 4 units:  f(x) = |-x - 4|

Horizontal stretch of sf 1/2:  f(x) = 1/2 |-x - 4|

Vertical translation up 5 units:  f(x) = 1/2 |-x - 4| + 5

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A 20-pound bag of dog food costs $16. What is the unit price per pound? ​
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0.8

Step-by-step explanation:

To calculate the cost of any item per pound, divide the cost of the item by its weight in pounds: cost ÷ pounds = cost per pound.

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3 years ago
Which expression has the same value as 37.4 - 54.9?
GrogVix [38]

Answer:

D

Step-by-step explanation:

In the original expression =  37.4 - 54.9 = -17.5

So, we have to solve all the equations but 1 of them has to equal to -17.5

A) -54.9 + (-37.4) = -92.3

   Remove parentheses

   = -54.9 - 37.4

Subtract the numbers

    -92.3

B) 54.9 - 37.4 = 17.5

Since 54.9 is greater than 37.4 just subtract normally

 4   14

  5  4.   9                < ------- Line up the decimal points like this

-  3  7.   4                <---------  Subtract the decimals

-----------------

   1   7   .    5       <---------- This is the final answer to B.                    

 

C)  37.4 - (- 54.9) = 92.3

   Change the sign to addition

        =37.4 + 54.9

  Add the numbers normally

  54.9

+ 37. 4

--------------

  92.3

D)  37.4 + (-54.9) = -17.5

   Change the sign to subtraction

      =    37.4 - 54.9

Subtract them normally (but as you can see you are subtracting a smaller number from a larger number so heres a trick that you can use switch the equation by putting the larger number in first like this....)

54.9 - 37.4 = 17.5 (REMEMBER the answer is not 17.5 because the original equation of D is reversed  37.4 - 54.9 so in this case your answer should be

- 17.5)

37.4 - 54.9 = -17.5

Your final answer is D because it matches 37.4 - 54.9.

Hope this helps!

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Step-by-step explanation:

7.75*10 = 77.5

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