Mathematics, 05.09.2020 20:01 adjjones2011

Which statements about the graph of the function f(x) = -x2 - 4x + 2 are true? Select three options. The domain is {x|x 5-2}.
The range is {yly s 6}.
The function is increasing over the interval (-0, -2).
The function is decreasing over the interval (-4, 00).
The function has a positive y-intercept.

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Answer from: jimissac68

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 .

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 .

It is upside down U, when a<0 .

So here we have a=-1 so a<0 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<0 ) or the lowest point (if ).

The vertex here will be the highest point, again since a<0 .

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

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 :

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

-0-0+2

0+2

The y-intercept is positive since 2>0.

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

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