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jok3333 [9.3K]
3 years ago
11

The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply.

Mathematics
2 answers:
strojnjashka [21]3 years ago
7 0
<span>The axis of symmetry is x = –4.
</span><span>The domain is all real numbers.
</span><span>The x-intercepts are at (–6, 0) and (–2, 0). </span>
mezya [45]3 years ago
5 0

Answer:

The correct options are 2, 3 and 6.

Step-by-step explanation:

The given function is

f(x)=x^2+8x+12

It is an upward parabola because the leading coefficient is positive.

The vertex of an upward parabola is the minimum value, therefore option 1 is incorrect.

Write the above function in vertex form.

f(x)=(x^2+8x)+12

If a polynomial is g(x)=x^2+bx then we add (\frac{b}{2})^2, to make it perfect square.

Here b=8 so we have to add 4^2.

f(x)=(x^2+8x+4^2)+12-4^2

f(x)=(x+4)^2-4              ... (1)

the vertex form of a parabola is

g(x)=a(x+h)^2+k              ... (2)

Where (h,k) is vertex, axis of symmetry is x=h, domain all real numbers, range y>k. Function is decreasing over (–∞, h) and the function is increasing over (h,∞).

From (1) and (2), we get

a=1,h=-4,k=-4

The vertex of the parabola is (-4,-4), axis of symmetry is x=-4, domain all real numbers, range y>-4. Function is decreasing over (–∞, -4) and the function is increasing over (-4,∞).

Substitute f(x)=0 in the given function, to find the x-intercepts.

0=x^2+8x+12

0=x^2+6x+2x+12

0=x(x+6)+2(x+6)

0=(x+2)(x+6)

x=-2,-6

Therefore the  x-intercepts are at (–6, 0) and (–2, 0).

Thus the correct options are 2, 3 and 6.

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Answer:

67

Step-by-step explanation:

● -(x + 3) + (y - 5) + (z - 6)

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8 0
3 years ago
Which of the following statements is true?
MakcuM [25]

Answer:

e. All of these statements are true.

Step-by-step explanation:

The first statement is true because an experiment is actually the process by which an observation is made. Consider rolling a die. It is called an experiment because we observe which side of the die lands facing upwards and that number is noted.

The second statement is also true because a simple event is the one which can not be further decomposed into an event. (Compound events can be decomposed into simple events).

The third statement is also true that an event is the collection of one or more simple events. An event can contain either simple events of compound events which are basically a combination of two or more simple events.

Hence, we can say that <u>all the statements are true</u>.

6 0
3 years ago
Find the probability of rolling a 6 on a number cube and flipping heads on a coin
serious [3.7K]

Assuming that the number cube is 6 sided

6 is one number in a 6 sided cube, so the probability is: 1/6

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1/6 x 1/2 = 1/12

1/12 is your probability

hope this helps

4 0
3 years ago
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Find the area of the figure below<br><br> A.832in^2<br> B.768^2<br> C.416^2<br> D.384in^2
lesantik [10]
The area is the average of the 2 heights times the base, which is:
(24+16)/2*19.2=384 in^2=D
6 0
2 years ago
what is the value of the x variable in the solution to the following system of equations? 2x 2y = 6 x 3y = −1 a. −2 b. 2 c. 5 d.
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2x + 2y = 6 . . . . . (1)
x + 3y = -1 . . . . . (2)

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(3) - (4) => 4x = 20
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7 0
3 years ago
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