1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Karolina [17]
2 years ago
14

Determine the equation of the graph, and select the correct answer below.

Mathematics
2 answers:
inysia [295]2 years ago
8 0

Answer:

Thus, (a) is correct.

y=-(x+1)^2+3 is the equation of the given graph

Step-by-step explanation:

Given a graph with vertex (-1 , 3)

We have to determine the equation of the graph and choose from the given options.

Since, the graph represents a quadratic equation.

The general form of representing a quadratic equation is y=a(x-h)^2+k , where (h,k) is the vertex. a determine whether the graph open ups or down if it is positive then it open upward and vice versa.

For the given graph, vertex (-1 , 3)

Substitute h = -1 and k = 3  in y=a(x-h)^2+k we get,

y=a(x+1)^2+3

Also the graph opens down ward so a has to be negative,

So y=-(x+1)^2+3

Thus, Option (a) is correct.

nignag [31]2 years ago
3 0
This answer is A. 
Basically, the parabola opens downward so you know that the equation has a negative in the front... 
You might be interested in
Question 3 of 10
mestny [16]

Answer:

㋡

Check Answer

♣ Qᴜᴇꜱᴛɪᴏɴ :

If tan θ = \sf{\dfrac{1}{\sqrt{7}}}

7

1

, Show that \sf{\dfrac{cosec ^2 \theta - sec ^2\theta}{cosec^2\theta + sec^2\theta }=\dfrac{3}{4}}

cosec

2

θ+sec

2

θ

cosec

2

θ−sec

2

θ

=

4

3

★═════════════════★

♣ ᴀɴꜱᴡᴇʀ :

We know :

\large\boxed{\sf{tan\theta=\dfrac{Height}{Base}}}

tanθ=

Base

Height

So comparing this formula and value of tan θ from question, we get :

Height = 1

Base = √7

Now we need to Prove the value of : \sf{\dfrac{cosec ^2 \theta - sec ^2\theta}{cosec^2\theta + sec^2\theta }=\dfrac{3}{4}}

cosec

2

θ+sec

2

θ

cosec

2

θ−sec

2

θ

=

4

3

Also :

\large\boxed{\sf{cosec\theta=\dfrac{Hypotenuse}{Height}}}

cosecθ=

Height

Hypotenuse

\large\boxed{\sf{sec\theta=\dfrac{Hypotenuse}{Base}}}

secθ=

Base

Hypotenuse

From this we get :

\large\boxed{\sf{cosec^2\theta=\left(\dfrac{Hypotenuse}{Height}\right)^2}}

cosec

2

θ=(

Height

Hypotenuse

)

2

\large\boxed{\sf{sec^2\theta=\left(\dfrac{Hypotenuse}{Base}\right)^2}}

sec

2

θ=(

Base

Hypotenuse

)

2

But we have Height and Base, we dont have Hypotenuse.

Hypotenuse can be found by using Pythagoras Theorem

Pythagoras Theorem states that :

Hypotenuse² = Side² + Side²

For our question :

Hypotenuse² = Height² + Base²

Hypotenuse² = 1² + √7²

Hypotenuse² = 1 + 7

Hypotenuse² = 8

√Hypotenuse² = √8

Hypotenuse = √8

➢ Let's find value's of cosec²θ and sec²θ

________________________________________

First cosec²θ :

\large\boxed{\sf{cosec^2\theta=\left(\dfrac{Hypotenuse}{Height}\right)^2}}

cosec

2

θ=(

Height

Hypotenuse

)

2

\sf{cosec^2\theta=\left(\dfrac{\sqrt{8}}{1}\right)^2}cosec

2

θ=(

1

8

)

2

\sf{cosec^2\theta=\dfrac{8}{1}}cosec

2

θ=

1

8

cosec²θ = 8

________________________________________

Now sec²θ :

\large\boxed{\sf{sec^2\theta=\left(\dfrac{Hypotenuse}{Base}\right)^2}}

sec

2

θ=(

Base

Hypotenuse

)

2

\sf{sec^2\theta=\left(\dfrac{\sqrt{8}}{\sqrt{7}}\right)^2}sec

2

θ=(

7

8

)

2

\sf{sec^2\theta=\dfrac{8}{7}}sec

2

θ=

7

8

sec²θ = 8/7

________________________________________

Now Proving :

\sf{\dfrac{cosec ^2 \theta - sec ^2\theta}{cosec^2\theta + sec^2\theta }=\dfrac{3}{4}}

cosec

2

θ+sec

2

θ

cosec

2

θ−sec

2

θ

=

4

3

Taking L.H.S :

\sf{\dfrac{cosec ^2 \theta - sec ^2\theta}{cosec^2\theta + sec^2\theta }}

cosec

2

θ+sec

2

θ

cosec

2

θ−sec

2

θ

=\sf{\dfrac{8 - sec ^2\theta}{8 + sec^2\theta }}=

8+sec

2

θ

8−sec

2

θ

=\sf{\dfrac{8 - \dfrac{8}{7}}{8 + \dfrac{8}{7} }}=

8+

7

8

8−

7

8

=\sf{\dfrac{\dfrac{48}{7}}{\dfrac{64}{7} }}=

7

64

7

48

\sf{=\dfrac{48\times \:7}{7\times \:64}}=

7×64

48×7

\sf{=\dfrac{48}{64}}=

64

48

\bf{=\dfrac{3}{4}}=

4

3

= R.H.S

Hence Proved !!!

7 0
2 years ago
F(x)=(x-2)(x+4) what is the y-intercept and x-intercept
GarryVolchara [31]

Answer:

x-int=-8, y-int=2,-4

Step-by-step explanation:

for the x-int

you set x to 0 then solve the equation to get -8

for the y-int

you set y(or in this case f(x)) to 0 then solve. You solve this by spilting this into 2 linear equations; x-2=0 and x+4=0, then you solve them both to get the two y-intercepts, 2 and -4

6 0
3 years ago
An aircraft costs $2954 dollars per hour to operate. The algebraic expression 2954t gives the total cost to operate the aircraft
sdas [7]
10,634.4 total cost



2954t t=3.6h. 2954 x 3.6 = 10,634.4 total cost
6 0
2 years ago
Kira received a $80 gift card for a coffee store. She used it in buying some coffee that cost $8.03 per pound. After buying the
never [62]

Answer:

5 pounds

Step-by-step explanation:

80 - 39.85 = 40.15

40.15 ÷ 8.03

= 5

3 0
1 year ago
The graph box linear function f passes through the point (1, -9) and has a slope of 3
Marat540 [252]

9514 1404 393

Answer:

  C) 4

Step-by-step explanation:

The point-slope equation of the line is ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y +9 = 3(x -1) . . . . . line with slope 3 through point (1, -9)

For y=0 (the 0 of the function), we have ...

  9 = 3(x -1)

  3 = x -1

  4 = x

The x-intercept is (4, 0).

3 0
2 years ago
Other questions:
  • If the radius of a cone is doubled and the height is tripled, what happens to the volume?
    5·1 answer
  • Using the data: 2, 2, 3, 3, 3, 4, 5, 6, 6, 10
    14·2 answers
  • The function f(t) represents the cost to connect to the Internet at an online gaming store. It is a function of t, the time in m
    9·2 answers
  • Find the area of the shaded region.
    5·1 answer
  • Would this expression be <br> 49+R?
    6·1 answer
  • Can someone help me I’m slow and not understanding
    15·1 answer
  • Can someone please help me
    10·2 answers
  • Find the total area round to the nearest 10th if necessary use the pi symbol on calculator
    5·1 answer
  • Help,anyone can help me do quetion​
    13·1 answer
  • 0.025 / 0.08 how do you do it so can you explain the steps​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!