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musickatia [10]
3 years ago
15

The image shows a geometric representation of the function f(x) = x2 – 2x – 6 written in standard form.

Mathematics
1 answer:
fenix001 [56]3 years ago
7 0
The vertex form of the equation of a parabole is (x - h)^2 + k

So you must complete squares to transform x^2 -2x - 6 in its vertex form.


1) convert x^2 - 2x in a square => (x - 1)^2 - 1

2) Add the constant term - 6 => (x - 1)^2 -1 - 6

3) Add similar terms => (x - 1)^2 - 7

You can verify that (x - 1)^2 - 7 is equal to x^2 - 2x - 6:

x^2 - 2x + 1 - 7 = x^2 - 2x - 6. So, do not doubt it, the vertex form is (x - 1)^2  - 7, where the coordinates of the vertex are (1, - 7)

Answer: option A (x - 1)^2 - 7
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I REALLY NEED HELP ON THIS PLS HELP
Eva8 [605]

Part (a)

Answer: See the attached image below to see the filled out chart.

Note how rational and irrational numbers have nothing in common. This means there is no overlap. So they go in the rectangles. The two sets of numbers join up to form the entire set of real numbers.

Integers are in the set of rational numbers. This is because something like 7 is also 7/1; however 1/7 is not an integer. So not all rational numbers are integers. The larger purple circle is the set of integers.

The smaller blue circle is the set of whole numbers. The set of whole numbers is a subset of integers. Recall the set of whole numbers is {0,1,2,3,...} so we ignore the negative values only focusing on 0 and positive numbers that don't have any fractional values. In contrast, the set of integers is {..., -3, -2, -1, 0, 1, 2, 3, ...} here we do include the negatives.

============================================================

Part (b)

1) Some irrational numbers are integers.

This is false. An irrational number is not rational. The set of integers is contained entirely in the set of rational numbers.

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

2) Some whole numbers are not irrational numbers.

This is false. The statement implies that some whole numbers are irrational, but the set of whole numbers is inside the set of rational numbers, which has no overlap with the irrationals. The statement should be "All whole numbers are not irrational numbers".

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

3) All rational numbers are whole numbers.

This is false. A rational number like 1/3 is not a whole number.

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

4) All integers are whole numbers

This is false. An integer like -44 is not a whole number because the set of whole numbers is {0,1,2,3,...} and we're not including negative values.

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

In summary, all four statements for part (b) are false.

8 0
2 years ago
Read 2 more answers
Simplify the following expression: -k - 11 - 2 + 2k​
gulaghasi [49]

Answer:

k-13

Step-by-step explanation:

brainliest?

5 0
3 years ago
Read 2 more answers
Can someone please help me
gtnhenbr [62]

Answer:

1) B) 10

2) B) 9

Step-by-step explanation:

1) 10x+15=115

10x=100

x=10

2) 12x+17=125

12x=108

x=9

8 0
3 years ago
the food bill for meal at a restaurant is $12. THe sales tax is 6.5%, and you leave 15% tip. Wat is the total cost of the meal?
jeka57 [31]

Answer:

Step-by-step explanation:

12*6.5%=0.72

12+15%=13.8

0.72+13.8=14.52

6 0
1 year ago
ben earns $9 per hour and $6 for each deilvery he makes.he wants to earn more than $155 in an 8-hour workday.what is the least n
barxatty [35]
So in a 8 hour workday he would make $72... 9x8=72
now 155-72= 83 
83/6= a little over 13
so he would at least have to make 14 deliveries 
:)
7 0
3 years ago
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