The question is on the picture

Axis of sym: x =

marta [7]

Answer:

<h2>SEE BELOW</h2>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>

quadratic function
PEMDAS

<h3>let's solve:</h3>

vertex:(h,k)

therefore

vertex:(-1,4)

axis of symmetry:x=h

therefore

axis of symmetry:x=-1

to find the quadratic equation we need to figure out the vertex form of quadratic equation and then simply it to standard form i.e ax²+bx+c=0

vertex form of quadratic equation:

y=a(x-h)²+k

therefore

y=a(x-(-1))²+4
y=a(x+1)²+4

it's to notice that we don't know what a is

therefore we have to figure it out

the graph crosses y-asix at (0,3) coordinates

so,

3=a(0+1)²+4

simplify parentheses:

$3 = a(1 {)}^{2} + 4$

simplify exponent:

$3 = a + 4$

therefore

$a = - 1$

our vertex form of quadratic equation is

y=-(x+1)²+4

let's simplify it to standard form

simplify square:

$y = - ( {x}^{2} + 2x + 1) + 4$

simplify parentheses:

$y = - {x}^{2} - 2x - 1 + 4$

simplify addition:

$y = - {x}^{2} - 2x + 3$

therefore our answer is D)y=-x²-2x+3

the domain of the function

$x\in \mathbb{R}$

and the range of the function is

$y\leqslant 4$

zeroes of the function:

$- {x}^{2} - 2x + 3 = 0$

$\sf divide \: both \: sides \: by \: - 1$

${x}^{2} + 2x - 3 = 0$

$\implies \: {x}^{2} + 3x - x + 3 = 0$

factor out x and -1 respectively:

$\sf \implies \: x(x + 3) - 1(x + 3 )= 0$

group:

$\implies \: (x - 1)(x + 3) = 0$

therefore

$\begin{cases} x_{1} = 1 \\ x_{2} = - 3\end{cases}$

4 0

2 years ago

Which functions domain consists of all real numbers except -2?

Eddi Din [679]

Answer:

option (a) f(x)= 1/x+2

Step-by-step explanation:

(a) f(x) = 1/ x+2

To find the restriction for domain , we set the denominator =0 and solve for x

x+2 =0, so x=-2

When x=-2 then denominator becomes 0 that is undefined.

So, domain is all real numbers except -2

(b) f(x)= 2x

In this function, there is no denominator or square root or log function

so there is no restriction for x, hence domain is all real numbers

(c) f(x) = 2x-2

In this function, there is no denominator or square root or log function

so there is no restriction for x, hence domain is all real numbers

f(x) = 1/ sqrt(x+2)

if we have square root in the denominator then we set the denominator >0 and solve for x. because square root of negative values are undefined

x+2>0, x>-2

Hence domain is all real numbers that are greater than -2

8 0

3 years ago

"if the standard deviation of a group of 20 scores is 15, what is the variance?"

DerKrebs [107]

We have been given that the standard deviation of a group of 20 scores is 15 and we are asked to find variance.

Since we know variance is square of standard deviation. In order to find out the variance of the given data we have to take the square of 15.

$\text{ Variance}=\sigma^{2}\\
=15^{2}=225$

Therefore, our variance is 225.

7 0

2 years ago

Help me assapppp!!! Pls

mafiozo [28]

Answer:

have you tries adding them together?

5 0

3 years ago

A maps key shows that every 5 inches on the map represents 200 miles of actual distance. Suppose the distance between two cities

ryzh [129]

Hello there, and thank you for posting your question here on brainly.

Short answer: 280 miles.

Why?

You can find this out by finding out how much 1 in is by dividing 200 by 5. (200 / 5 ==> 40) So 1 in = 40 miles. Now, we multiply that by 7, so we can find out how much 7 in would be. (7 * 4 ==> 280) 7 inches on the map represents 280 miles.

Hope this helped you! ♥

3 0

2 years ago