What is the range of the function graphed below ?

Answer:

Step-by-step explanation:

The standard form of parabola having vertex ( 2 , 5) is given by y = [tex]\frac{1}{4}[/tex] ( x - 2 )² + 5.

What is a parabola ?

A parabola is a plane curve that is produced when a point moves so that its distance from a given point equals its distance from a fixed line.

We know that , the standard form or general equation of a parabola is given by :

y  = a ( x - h )² + k

where : vertex is (h, k) and focus ( h , k + p)

We know that here directrix is y = k - p and a is a = [tex]\frac{1}{4p}[/tex]

It is given that focus is (2 , 6).

From focus :

h = 2 and k + p = 6

whereas from directrix :

k - p = 4

Adding both

k + p = 4

k - p = 6

We get :

2k = 10

or

k = 5

So ,

p = 1

And vertex will be :

(h , k) = (2 , 5).

The vertical distance from vertex to directrix p = 1 :

y  = a ( x - 2 )² + 5

here , a = [tex]\frac{1}{4p}[/tex] or a = 1/4

So , the standard form of given parabola will be :

y = [tex]\frac{1}{4}[/tex] ( x - 2 )² + 5

Therefore , the standard form of parabola having vertex ( 2 , 5) is given by y = [tex]\frac{1}{4}[/tex] ( x - 2 )² + 5.

Learn more about parabola here :

https://brainly.com/question/14502549

#SPJ2

Answer:

x = 30

General Formulas and Concepts:

Pre-Alg

Step-by-step explanation:

Step 1: Define equation

8x - 3(2x - 4) = 3(x - 6)

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

it would be -4 i think

come back and tell me if im wrong

Answer:

The required answer is [tex]y=-\mathbf{\frac{3}{2}}x\\[/tex]

Step-by-step explanation:

We are given that value of x and y vary directly so , if two values vary directly we can write

y∝x

y=kx

Now, we are given x=-4 and y=6 and we have to fill in the blank. We actually have to find value of k i.e y=____x . Yhe blanks must be filled by value of k because y=kx

Using values of x and y i.e x=-4 and y=6 to find value of k

[tex]y=kx\\6=k(-4)\\Divide \ both \ sides \ with \ -4\\\frac{6}{-4}= \frac{k(-4)}{-4} \\k=\frac{-3}{2}[/tex]

The value of k is [tex]\mathbf{\frac{-3}{2}}[/tex]

So, the required answer is [tex]y=-\mathbf{\frac{3}{2}}x\\[/tex]

Answer:

Step-by-step explanation:

I would use the Horner method.

f(x) = x³ – 3x² – 10x + 24

f(2) = 2³ - 3·2² - 10·2 +24 = 0   ⇒ x=2 is the root of function

So:

    |   1   | -3   |  -10  |  24 |

2  |   1   |  -1   |  -12  |  0   |

therefore:

f(x) = x³ – 3x² – 10x + 24 =  (x – 2)(x² – x – 12)

For  x² – x – 12:

[tex]x=\dfrac{1\pm\sqrt{(-1)^2-4\cdot1\cdot(-12)}}{2\cdot1}=\dfrac{1\pm\sqrt{1+48}}{2}=\dfrac{1\pm7}{2}\\\\x_1=\dfrac{1+7}{2}=4\ ,\qquad x_2=\dfrac{1-7}{2}=-3[/tex]

It means:

f(x) = x³ – 3x² – 10x + 24 =  (x – 2)(x – 4)(x + 3)

Answer:

Hi,

LHS = sinA-cosA+1/sinA+cosA-1

divide both numerator and denominator by cosA

LHS=(tanA−1+secA)/(tanA+1−secA)LHS=(tanA−1+secA)/(tanA+1−secA)

Now

sec2A=1+tan2Asec2A=1+tan2A

sec2A−tan2A=1sec2A−tan2A=1

Using above relation at denominator of LHS

LHS=(tanA−1+secA)/(tanA−secA+sec2A−tan2A)LHS=(tanA−1+secA)/(tanA−secA+sec2A−tan2A)

LHS=(tanA−1+secA)/((secA−tanA)(−1+secA+tanA))LHS=(tanA−1+secA)/((secA−tanA)(−1+secA+tanA))

LHS=1/(secA−tanA)LHS=1/(secA−tanA)

LHS=RHSLHS=RHS

Hence Proved.

I think above proof will clear your doubt,

All the best.

Answer:

3.96 months or close to 4 months

Step-by-step explanation:

[tex]\frac{33}{100} *\frac{x}{12}[/tex]

Cross multiply

396 = 100x

Divide both sides by 100 to get x alone

396/100 = 100x/100

3.96 = x

Hope this helps and pls do mark me brainliest:)

Answer:

3.96 or 4 rounded

Step-by-step explanation:

4 because is you multiply 12*.33 = 3.96

If you round it is 4 months.

Hope this helps!!

Using the formula

A=wl

Solving for w

w=A

l=28

6≈4.66667 or 4.67

hope it helps! :3

Also, I want to point out the fact that your profile picture is Todoroki. I love him. He is my favorite character in mha. It is nice to meet a fellow fan. Especially since I had to deal with my friend saying the show sucks...

Answer:

The price for 1 lemon is $0.75

Step-by-step explanation:

8x=$6

8x/8=6/8

x=$0.75

Answer:

90

Step-by-step explanation:

it looks like it's a right angle

Answer:

The answer is 90 degrees

Step-by-step explanation:

Answer:

C) JFG BECAUSE THAT IS WERE IT CROSSES AT

Answer:

the origen is where they all start

Answer:

(a) The coordinates of the inflection point are (1; 8) and, being the value of a less than zero, then these coordinates indicate the maximum of the function.

(b) The y-intercept has a value of 6

(c) The coordinates of the x-intercepts have a value of x=3 and x=-1

Step-by-step explanation:

You know y= -2*(x-1)² + 8

(a) Every quadratic function can be expressed by the canonical form:

f(x)=y= a*( x- h)² + k

where a is the principal coefficient and the ordered pair (h; k) are the coordinates of the vertex of the parabola.

The quadratic function will have a maximum or minimum value at the vertex. If a> 0, the parabola is concave, that is, it will have its branches upwards, therefore the vertex will indicate the minimum of the function. But if a <0 the parabola is convex and the vertex will indicate the maximum of the function.

Comparing the given equation with the canonical form of a quadratic function you can see that:

Then, the coordinates of the inflection point are (1; 8) and, being the value of a less than zero, then these coordinates indicate the maximum of the function.

(b)  The y-intercept arises from evaluating the function at x = 0. So, in this case:

y= -2*(0-1)² + 8

Solving:

y= -2*(-1)² + 8

y= -2*1 + 8

y= -2+8

y= 6

The y-intercept has a value of 6

(c)   The roots or coordinates of the x-intercepts arise from evaluating the function at y = 0. So, in this case:

0= -2*(x-1)² + 8

Solving:

-8= -2*(x-1)²

[tex]\frac{-8}{-2} =(x-1)^{2}[/tex]

4= (x-1)²

√4= |x-1|

⇒ 2=x-1 → 2+1=x → 3=x

⇒ -2=x-1 → -2+1=x → -1=x

The coordinates of the x-intercepts have a value of x=3 and x=-1

Answer:

r≈0.5m

Step-by-step explanation:

she was right

Answer:

r≈0.5m

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

Answer:

X cubed plus one

Step-by-step explanation:

Answer:

The answer is 6/8

Step-by-step explanation:

6/8 is the only logical answer because you need to have an answer that is less than one, 8/6 evens out to 1 1/3, 6/2 evens out to 3, and 8/4 evens out to 2. 6/8 is the only fraction that is less than one.

Answer:

its 6/8

Step-by-step explanation:

Answer: 3x+12y+4

Step-by-step explanation:

The only like terms are the x+2x so we add them to get the simplfied answer

Answer:

3x + 12y + 4

I dont really know how to explain but since there is an X at the and of the 2, you can add X + 2x to get 3x. Since 3x, 12y, and 4 are not alike, this is the simplest form.

Answer:

Parralel lines have the exact same slope.

in the equation y=mx+b m is the slope

Both of these equations are in slope intercept form (y=mx+b) meaning that the coefficient in both equations is the slope.

Parralel lines have the same slope and perpendicular lines have the inverse opposite slope. For example if a line had a slope of 2 or 2/1 then the perpendicular line to it would have a slope of -1/2.

With that knowledge we can easily see that the lines are perpendicular since their slopes (represented by the coefficient) are the inverse opposite.

Perpendicular is your answer

Step-by-step explanation:

Answer:

Distrubutative property

Step-by-step explanation:

Answer:

$5.94

Step-by-step explanation:

Multiply 2.75 by $0.76 to get $2.09

Multiply 2.75 by $1.40 to get $3.85

Add $3.85 and $2.09 to get $5.94

Answer:

$5.94

Step-by-step explanation:

Answer:

The area is 225 and they are not directly proportional

Step-by-step explanation:

find the area by doing 15 x 15 which is 225

Answer:

225

Step-by-step explanation:

easy

Answer:

(1, 3)

Step-by-step explanation:

Answer: B. 1, 3

Step-by-step explanation: On Edge!!!!