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
11Alexandr11 [23.1K]
3 years ago
10

What is the vertex of the function?

Mathematics
1 answer:
Romashka [77]3 years ago
8 0

Answer:

  (4, -25)

Step-by-step explanation:

One way to answer this is to put the equation into vertex form.

  f(x)= x^2 -8x -9 . . . . . given

Add and subtract the square of half the x-coefficient:

  f(x) = x^2 -8x +(-8/2)^2 -9 -(-8/2)^2

  f(x) = x^2 -8x +16 -25

  f(x) = (x -4)^2 -25

Comparing this to the vertex form of a quadratic:

  f(x) = a(x -h)^2 +k

we find that (h, k) = (4, -25). This is the vertex.

_____

<em>Alternate solution</em>

The line of symmetry for ...

  f(x) = ax^2 +bx +c

is given by x = -b/(2a). For your given quadratic that line is ...

  x = -(-8)/(2(1)) = 4

Evaluating f(4) gives the y-coordinate:

  f(4) = 4^2 -8·4 -9 = -25

The vertex is (x, y) = (4, -25).

You might be interested in
Divide fractions: 5/6 divided by 6/10 (leave as improper fraction if necessary)
tankabanditka [31]

Answer:

25/18

Step-by-step explanation:

5/6 / 6/10

K    C    F

5/6 * 10/6

50/36 = 25/18

5 0
3 years ago
Solve for x: 4 over 5 x + 4 over 3 = 2x x = __________________ Write your answer as a fraction in simplest form. Use the "/" sym
alexgriva [62]
Let's see.

4x/5 + 4/3 = 2x

First we have to make each denominator the same, so I'll multiply 4x/5 by 3/3, 4/3 by 5/5, and 2x by 15/15

Now we have 12x/15 + 20/15 = 30x/15

With everything in the same denominator we can solve the new equation of
12x + 20 = 30x

20 = 18x

10 = 9x

X= 10/9
5 0
3 years ago
Read 2 more answers
24+4(3+1) I know the answer but I need to show my work can anyone show me how they got the answer cause the answer is 40 but I d
solong [7]
24 + 4(3 + 1)
= 24 + 4(4)
=24+ 16
= 40
6 0
2 years ago
Read 2 more answers
Please help me im crying over this question
denis23 [38]

Answer:

y = 2x - 2

Step-by-step explanation:

y= mx+b

m= slope

b= y-intercept (point on line where x= 0.... or the point where the line hits the y-axis)

Determine slope by using slope formula or by counting boxes

By counting boxes, you can see that each point is 2 units up, 1 unit right (2/1)

the slope is 2

the point where the line is touching the y-axis is (0, -2)

m = slope = 2

b  = y-intercept = -2

y = 2x + (-2) OR y = 2x -2

5 0
3 years ago
If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (
Andrew [12]

Answer:

The function h (x) = StartFraction 11 Over x minus 4 EndFraction

has the domain of h (x) = ( - ∞, 4) U (4, ∞ ) which is same as the

domain of (m ∘ n)(x) = ( - ∞, 4) U (4, ∞ ).

Step-by-step explanation:

m (x) = StartFraction x + 5 Over x minus 1 and n(x) = x – 3

As m (x) could be written as:

m(x) = \frac{x+5}{x-1}

n(x) = x – 3

(m ∘ n)(x) = m(n(x)) = m(x – 3)

              = \frac{(x-3) + 5}{(x-3) - 1}

              = \frac{x+2}{x-4}

In order to find the domain of (m ∘ n)(x) = \frac{x+2}{x-4}, we need to

make sure that denominator can not be zero,

So,

     x - 4 = 0

     x = 4    

So, our domain can be anything except for 4.

Hence, Domain = D = ( - ∞, 4) U (4, ∞ )

Now, compare the domain of (m ∘ n)(x) i.e D = ( - ∞, 4) U (4, ∞ ) with all the options:

Option A: h (x) = x + 5 / 11

Option A has the Domain of h (x) = Set of all real numbers

So, Option A is false.

Option B: h (x) = 11 / x - 1

                        x - 1 = 0

                         x = 1

Option B has the domain of h (x) = ( - ∞, 1) U (1, ∞ )

So, Option B is false.

Option C: h (x) = 11 / x - 4

                        x - 4 = 0

                         x = 4

Domain C has the domain of h (x) = ( - ∞, 4) U (4, ∞ )

So, Option C is true.

Option D: h (x) = 11 / x - 3

                        x - 3 = 0

                         x = 3

Option D has the domain of h (x) = ( - ∞, 3) U (3, ∞ )

So, option D is also false.

Hence, only option C is true as the option C i.e. h (x) = StartFraction 11 Over x minus 4 EndFraction has the domain of h (x) = ( - ∞, 4) U (4, ∞ ) which is same as the domain of (m ∘ n)(x) = ( - ∞, 4) U (4, ∞ ).

keywords: Domain, composite function

Learn more about the domain of function from brainly.com/question/13020740

#learnwithBrainly

4 0
3 years ago
Read 2 more answers
Other questions:
  • 3135 divided 5 and 1052 divided 4
    12·2 answers
  • Write the equation of line in slope-intercept form, which is parallel to y=−2x+5 and passing through the point (1, −4).
    14·1 answer
  • 2x²+10x+12 factor. how do I find the solution?
    14·1 answer
  • What is the common difference for this arithmetic sequence? 54, 50, 46, 42, 38, A. 34 B. 4 C. 54 D. -4
    7·2 answers
  • What is the degree of the following polynomial?<br> 3x^4 - 9x^2 + 12x^7 - 9x
    7·1 answer
  • The fact family model represents 6 + 5 = 11.
    7·1 answer
  • At the beginning of the month, Hercules had 96 violas in his store. He sold 9 violas during the month. What is the ratio of the
    15·1 answer
  • Divide. help due its 11:59 tonight
    5·1 answer
  • HELPPP PLEASE Here are two number line diagrams.
    12·2 answers
  • Can anyone answer this question for me.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!