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
serious [3.7K]
3 years ago
14

Y=-1/3x^2-4x-5 in vertex form

Mathematics
1 answer:
grigory [225]3 years ago
8 0

Answer:

Y=-\frac{1}{3}(x+6)^2+7   [Vertex form]

Step-by-step explanation:

Given function:

Y=-\frac{1}{3}x^2-4x-5

We need to find the vertex form which is.,

y=a(x-h)^2+k

where (h,k) represents the co-ordinates of vertex.

We apply completing square method to do so.

We have  

Y=-\frac{1}{3}x^2-4x-5

First of all we make sure that the leading co-efficient is =1.

In order to make the leading co-efficient is =1, we multiply each term with -3.

-3\times Y=-3\times\frac{1}{3}x^2-(-3)\times4x-(-3)\times 5

-3Y=x^2+12x+15

Isolating x^2 and x terms on one side.

Subtracting both sides by 15.

-3Y-15=x^2+12x-15-15

-3Y-15=x^2+12x

In order to make the right side a perfect square trinomial, we will take half of the co-efficient of x term, square it and add it both sides side.  

square of half of the co-efficient of x term = (\frac{1}{2}\times 12)^2=(6)^2=36

Adding 36 to both sides.

-3Y-15+36=x^2+12x+36

-3Y+21=x^2+12x+36

Since x^2+12x+36 is a perfect square of (x+6), so, we can write as:

-3Y+21=(x+6)^2

Subtracting 21 to both sides:

-3Y+21-21=(x+6)^2-21

-3Y=(x+6)^2-21

Dividing both sides by -3.

\frac{-3Y}{-3}=\frac{(x+6)^2}{-3}-\frac{21}{-3}

Y=-\frac{1}{3}(x+6)^2+7   [Vertex form]

You might be interested in
please help. answer is 62.1m(squared) and the objects are composite! please show the work, no matter what i do i cant seem to ge
yuradex [85]

Answer:

SA=62.1\ m^2

Step-by-step explanation:

step 1

Find the surface area of the smaller rectangular prism

SA=2B+Ph

where

B is the area of the base

P is the perimeter of the base

h is the height of the prism

SA=2[(2.5)(1.5)]+2(2.5+1.5)(1.5)

SA=7.5+12=19.5\ m^2

step 2

Find the surface area of the cube

SA=6s^2

where

s is the length side of the cube

SA=6(2.5^2)=37.5\ m^2

step 3

Find the lateral area of the cylinder

LA=\pi DL

where

D is the diameter of the base

L is the length of cylinder

LA=(3.14)(0.5)(3.5)=5.495\ m^2

step 4

Find the area of the base of cylinder

A=\pi r^{2}

we have

r=0.5/2=0.25\ m ----> the radius is half the diameter

A=(3.14)(0.25)^{2}=0.19625\ m^2

step 5

Find the surface are of the composite figure

we know that

The surface area of the composite figure is equal to the surface area of the smaller rectangular prism plus the lateral area of the cylinder, plus the surface area of the cube, minus the area of the two bases of cylinder

so

SA=19.5+5.495+37.5-2(0.19625)=62.1\ m^2

5 0
3 years ago
Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!
Drupady [299]

Answer:

6

Step-by-step explanation:

f(6) = -6   this is the value when the x value is 6

g(5) = -5 this is the value when the x value is 5

4 * f(6) -6*g(5)

4*-6 - 6* -5

-24 + 30

6

5 0
3 years ago
Read 2 more answers
ASAP
mojhsa [17]

Answer:

cost = 8p + 5

Step-by-step explanation:

$8*[number of pizzas] + $5 delivery fee

$8p + $5

8p + 5

cost = 8p + 5

3 0
2 years ago
Read 2 more answers
What is the slope of the line that passes<br> through the points (-3,-2) and (2,-4)?
marta [7]

Answer:

Formula of the slope of the line

m=(y2-y1)/(x2-x1)

y2= -1, y1 = 4

x2=5, x1 = -2

m=(-1-4)/(5-(-2)) = -5/7

Answer is D. slope = -5/7

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Find the midpoint P(16,7) and Q(12, -3) With work.
hichkok12 [17]

Answer:

(14, 2 )

Step-by-step explanation:

Use the midpoint formula

[0.5(x₁ + x₂), 0.5(y₁ + y₂) ]

with (x₁, y₁ ) = (16, 7) and (x₂, y₂ ) = (12, - 3)

midpoint = [0.5(16 + 12), 0.5(7 - 3) ] = [0.5(28), 0.5(4) ] = (14, 2 )

8 0
3 years ago
Read 2 more answers
Other questions:
  • keisha runs each lap in 8 minutes. she will run less than 7 laps today. what are the possible numbers of minutes she will run to
    6·2 answers
  • Nelson is fixing up office and must spend less than $7,500 to hire carpenters and painters. Carpenters charge $28 per hour and p
    9·1 answer
  • 47<br>22- +2353<br>soln<br>22- +2353​
    14·1 answer
  • Which one weighs more a pound of bricks or a pound of cotton balls?
    12·2 answers
  • 20 POINTS
    12·1 answer
  • The figure shows three quadrilaterals on a coordinate grid: A coordinate plane is shown. Quadrilateral D has sides measuring 3 u
    13·1 answer
  • Maximizing revenue. Edwards University wants to determine what price to charge for tickets to football games. At $18 per ticket,
    11·1 answer
  • I neeed helppp this is so confusing
    6·1 answer
  • Please list the transformations for the function <img src="https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx%2B2%7D%7Bx%2B5%7D%2B2" id="Te
    10·2 answers
  • PLEASEE HELPP IM DESPERATE I’LL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST CORRECTLY
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!