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AlexFokin [52]
3 years ago
14

Which statements about the graph of the function f(x) = -x2 - 4x + 2 are true? Select three options.

Mathematics
1 answer:
Nady [450]3 years ago
8 0

Answer:

Domain is all real numbers.

The range is \{y|y\le 6\}

The function is increasing over (-\infty,-2).

The function is decreasing over (-2,\infty)

The function has a positive y-intercept.

-----------------This is a guess if I had interpreted your choices correctly:

Second option: The range is \{y|y\le 6\}

Third option:  The function is increasing over (-\infty,-2).

Last option:  The function has a positive y-intercept.

I can't really read some of your choices. So you can read my above and determine which is false. If you have a question about any of what I said above please let me know.

Note: I guess those 0's are suppose to be infinities? I hopefully your function is f(x)=-x^2-4x+2.

Step-by-step explanation:

f(x)=-x^2-4x+2 is a polynomial function which mean it has domain of all real numbers.  All this sentence is really saying is that there exists a number for any value you input into -x^2-4x+2.

Now since the is a quadratic then it is a parabola. We know it is a quadratic because it is comparable to ax^2+bx+c, a \neq 0.

This means the graph sort of looks like a U or an upside down U.

It is U, when a>0.

It is upside down U, when a.

So here we have a=-1 so a which means the parabola is an upside down U.  

Let's look at the range.  We know the vertex is either the highest point (if a) or the lowest point (if a>0).

The vertex here will be the highest point, again since a.

The vertex's x-coordinate can be found by evaluating \frac{-b}{2a}:

\frac{-(-4)}{2(-1)}=\frac{4}{-2}=-2.

So the y-coordinate can be found by evaluate -x^2-4x+2 for x=-2:

-(-2)^2-4(-2)+2

-(4)+8+2

4+2

6

So the highest y-coordinate is 6.  The range is therefore (-\infty,6].

If you picture the upside down U in your mind and you know the graph is symmetrical about x=-2.

Then you know the parabola is increasing on (-\infty,-2) and decreasing on (-2,\infty).

So let's look at the intevals they have:

So on (-\infty,-2) the function is increasing.

Looking on (-4,\infty) the function is increasing on (-4,-2) but decreasing on the rest of that given interval.

The function's y-intercept can be found by putting 0 in for x:

-(0)^2-4(0)+2

-0-0+2

0+2

2

The y-intercept is positive since 2>0.

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  (-11, -8)

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Reflection across the x-axis changes the sign of the y-coordinate.

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in circle O the radius is 4ft and the measure of minor arc ab is 120 degrees find the length of minor arc ab to the nearest inte
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The circumference of a circle is given by 2\pi r, where r is the radius of the circle. Therefore, the circumference of the circle is 2\pi(4)=8\pi. As we found earlier, the length of the arc is \frac{1}{3} of this circumference. Therefore, the arc's length is 8\pi\cdot \frac{1}{3}=\frac{8\pi}{3}.

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Point G is the centroid of the right △ABC with m∠C=90° and m∠B=30°. Find AG if CG=4 ft.
o-na [289]

Answer: \text{Length of AG=}\frac{2\sqrt{63}}{3}

Explanation:  

Please follow the diagram in attachment.  

As we know median from vertex C to hypotenuse is CM  

\therefore CM=\frac{1}{2}AB

We are given length of CG=4  

Median divide by centroid 2:1  

CG:GM=2:1  

Where, CG=4

\therefore GM=2 ft

Length of CM=4+2= 6 ft  

\therefore CM=\frac{1}{2}AB\Rightarrow AB=12

In \triangle ABC, \angle C=90^0

Using trigonometry ratio identities  

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BC=AB\cos 30^0\Rightarrow BC=6\sqrt{3} ft  

CN=\frac{1}{2}BC\Rightarrow CN=3\sqrt{3} ft

In \triangle CAN, \angle C=90^0  

Using pythagoreous theorem  

AN=\sqrt{6^2+(3\sqrt{3})^2\Rightarrow \sqrt{63}

Length of AG=2/3 AN

\text{Length of AG=}\frac{2\sqrt{63}}{3} ft


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