8x-12y=84 into slope intercept form

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

Nady [450]

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.

8 0

3 years ago

Absolute value of 35+|-35|=

Effectus [21]

Answer is 70

Absolute value is just the positive value so 35+35 = 70

3 0

3 years ago

Read 2 more answers

Trisha and Byron are washing and vacuuming cars to raise money for a class trip. Trisha raised $38 washington 5 cars and vacuumi

ANEK [815]

Answer:

They charged $6 for washing and $2 for vacuuming the car.

Step-by-step explanation:

Let the charge of washing a car be 'x'.

And also let the charge of vacuuming a car be 'y'.

Now according to question, Trisha raised $38 washing 5 cars and vacuuming 4 cars.

So framing the above sentence in equation form, we get;

$5x+4y=38\ \ \ \ \ equation\ 1$

Again according to question, Byron raises $28 by washing 4 cars and vacuuming 2 cars.

So framing the above sentence in equation form, we get;

$4x+2y=28\ \ \ \ \ equation\2$

Now multiplying equation 2 by '2', we get;

$2(4x+2y)=28\times2\\\\8x+4y=56\ \ \ \ equation\ 3$

Now we subtract equation 1 from equation 3 and get;

$(8x+4y)-(5x+4y)=56-38\\\\8x+4y-5x-4y=18\\\\3x=18\\\\x=\frac{18}{3}=6$

Now substituting the value of 'x' in equation 1, we get;

$5x+4y=38\\\\5\times6+4y=38\\\\30+4y=38\\\\4y=38-30=8\\\\y=\frac{8}{4}=2$

Hence They charged $6 for washing and $2 for vacuuming the car.

8 0

3 years ago

Order these decimals from smallest to largest 1.89 -0.81 -2.6 0.24 -1.7

tiny-mole [99]

Answer:

-2.6, -1.7, -0.81, 0.24, 1.89

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Which phrase describes the pattern? 1, 3, 11, 123,...

Monica [59]

D) square the number and add 2

7 0

3 years ago

Read 2 more answers