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
Zigmanuir [339]
3 years ago
6

13. Find the vertex of f(x)=x2 -6x +8 .

Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
6 0

9514 1404 393

Answer:

  a  (3,-1)

Step-by-step explanation:

The number that "completes the square" is the square of half the x-coefficient, (-6/2)^2 = 9. Rearranging the given function to include the square trinomial, we have ...

  f(x) = x^2 -6x +9 -1 . . . . . . . here, we have 8 = 9 - 1

  f(x) = (x -3)^2 -1 . . . . . . . . . . vertex form

Comparing this to the generic vertex form ...

  f(x) = (x -h)^2 +k . . . . . . . vertex at (h, k)

we see that h=3 and k=-1.

The vertex is (h, k) = (3, -1).

You might be interested in
A nut wholesaler sells a mix of peanuts and cashews. He charges $2.80 per pound for peanuts and $5.30 per pound for cashews. If
Len [333]

Answer: 20 pounds of peanuts and 80 pounds of cashews.

5 0
3 years ago
Read 2 more answers
An Explanation Or Answer?
Delicious77 [7]
<span>4x + 1 ≥ 5
x</span><span>≥1
Answer: </span><span>{1, 2, 3}</span>
6 0
3 years ago
Read 2 more answers
How many pairs of potential clients can be randomly chosen from the pool of eight candidates?
sweet [91]
1 12 13 14 15 16 17 18
2 23 24 25 26 27 28
3 34 35 36 37 38
4 45 46 47 48
5 56 57 58
6 67 68
7 78
8
approximately 28 pairs. (breakdown above) hope this helps

4 0
3 years ago
Read 2 more answers
A football is thrown from the top of the stands, 50 feet above the ground at an initial velocity of 62 ft/sec and at an angle of
Anvisha [2.4K]

a. i. The parametric equation for the horizontal movement is x = 43.84t

ii. The parametric equation for the vertical movement is y = 50 + 43.84t

b. the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

<h2>a. Parametric equations</h2>

A parametric equation is an equation that defines a set of quantities a functions of one or more independent variables called parameters.

<h3>i. Parametric equation for the horizontal movement</h3>

The parametric equation for the horizontal movement is x = 43.84t

Since

  • the angle of elevation is Ф = 45° and
  • the initial velocity, v = 62 ft/s,

the horizontal component of the velocity is v' = vcosФ.

So, the horizontal distance the football moves in time, t is x = vcosФt

= vtcosФ

= 62tcos45°

= 62t × 0.7071

= 43.84t

So, the parametric equation for the horizontal movement is x = 43.84t

<h3>ii Parametric equation for the vertical movement</h3>

The parametric equation for the vertical movement is y = 50 + 43.84t

Also, since

  • the angle of elevation is Ф = 45° and
  • the initial velocity, v = 62 ft/s,

the vertical component of the velocity is v" = vsinФ.

Since the football is initially at a height of h = 50 feet, the vertical distance the football moves in time, t relative to the ground is y = 50 + vsinФt

= 50 + vtcosФ

= 50 + 62tsin45°

= 50 + 62t × 0.7071

= 50 + 43.84t

<h3>b. Location of football at maximum height relative to starting point</h3>

The location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

Since the football reaches maximum height at t = 1.37 s

The x coordinate of its location at maximum height is gotten by substituting t = 1.37 into x = 48.84t

So, x = 43.84t

x = 43.84 × 1.37

x = 60.0608

x ≅ 60.1 ft

The y coordinate of the football's location at maximum height relative to the ground is y = 50 + 48.84t

The y coordinate of the football's location at maximum height relative to the starting point is y - 50 = 48.84t

So,  y - 50 = 48.84t

y - 50 = 43.84 × 1.37

y - 50 = 60.0608

y - 50 ≅ 60.1 ft

So, the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

Learn ore about parametric equations here:

brainly.com/question/8674159

5 0
2 years ago
Mr Smith takes orders from 12 people. 8 people want coffee and 6 people want donuts. how many people want coffee and donuts?
PIT_PIT [208]

Answer:

2

Step-by-step explanation:

8 + 6 - 12 = 2

5 0
3 years ago
Other questions:
  • The spinner below is spun 20 times. It lands on red 6 times, yellow 2 times, green 8 times, and blue 4 times.
    12·1 answer
  • A researcher is interested in finding a 90% confidence interval for the mean number of times per
    9·1 answer
  • If ƒ(x ) = x 2 + 1, find ƒ(a + 1).
    8·1 answer
  • How many calories equal a pound?
    12·2 answers
  • Definitons: 1) Expand (multiply over brackets) 2) collecting like terms 3) rearranging 4) solving equations
    6·2 answers
  • - 7/9 • 5/7 <br> And subscribed to my YouTube alyha_diys
    8·2 answers
  • What is 5,100,000 in scientific notation?
    13·2 answers
  • Jennifer can run 12 miles in 2 hours, and she can bike 33 miles in 3 hours. What is Jennifer’s biking speed?
    13·1 answer
  • PLZ ANSWER THIS. I really need help from smart people.
    5·1 answer
  • The mean weight of 15 members of a company is 58kg. One more member whose weight is 74kg joins the company.Find the new mean wei
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!