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
Triss [41]
3 years ago
10

SOMEONE PLZ HELP ME!!!! I WILL GIVE BRAINLIEST!!!

Mathematics
1 answer:
MAXImum [283]3 years ago
6 0

Answer:

Step-by-step explanation:

Let the quadratic equation of the function by the points in the given equation is,

f(x) = ax² + bx + c

If the points lying on the graph are (-3, -10), (-4, -8) and (0, 8),

For (0, 8),

f(0) = a(0)² + b(0) + c

8 = c

For a point (-3, -10),

f(-3) = a(-3)² + b(-3) + 8

-10 = 9a - 3b + 8

9a - 3b = -18

3a - b = -6 --------(1)

For (-4, -8),

f(-4) = a(-4)² + b(-4) + 8

-8 = 16a - 4b + 8

-16 = 16a - 4b

4a - b = -4 ------(2)

Subtract equation (1) from equation (2)

(4a - b) - (3a - b) = -4 + 6

a = 2

From equation (1),

6 - b = -6

b = 12

Function will be,

f(x) = 2x² + 12x + 8

     = 2(x² + 6x) + 8

     = 2(x² + 6x + 9 - 9) + 8

     = 2(x² + 6x + 9) - 18 + 8

     = 2(x + 3)² - 10

By comparing this function with the vertex form of the function,

y = a(x - h)² + k

where (h, k) is the vertex.

Vertex of the function 'f' will be (-3, -10)

And axis of symmetry will be,

x = -3

From the given graph, axis of the symmetry of the function 'g' is; x = -3

Therefore, both the functions will have the same axis of symmetry.

y-intercept of the function 'f' → y = 8 Or (0, 8)

y-intercept of the function 'g' → y = -2 Or (0, -2)

Therefore, y-intercept of 'f' is greater than 'g'

Average rate of change of function 'f' = \frac{f(b)-f(a)}{b-a} in the interval [a, b]

                                                               = \frac{f(-3)-f(-6)}{-3+6}

                                                               = \frac{-10-8}{3}

                                                               = -6

Average rate of change of function 'g' = \frac{g(b)-g(a)}{b-a}

                                                                = \frac{g(-3)-g(-6)}{-3+6}

                                                                = \frac{7+2}{-3+6}

                                                                = 3

Therefore, Average rate of change of function 'f' is less than 'g'.

You might be interested in
If Carl, Steve and John have 40 sweets to share and John gets the most out of all three. What’s the smallest amount he can get?
Basile [38]

Answer:

13 +13 +14 ensures he is getting the smallest amount so its 14

Step-by-step explanation:

6 0
3 years ago
H(x)=4|x+4|+3 what’s the answer
MatroZZZ [7]

Answer:

To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.

Parent Function:

g(x)=|x|

Horizontal Shift: Right 4 Units

Vertical Shift: Up 1 Units

Reflection about the x-axis: None

Vertical Compression or Stretch: None

Step-by-step explanation:

4 0
2 years ago
For this graph mark the statements that are true
Nitella [24]

For the graph in the figure

we know that

the function  is a quadratic equation ( vertical parabola) open up

so

The vertex is a minimum

the vertex is the point (1,0)

The domain x of the function is all real numbers-------> (-∞,∞)

The range is the interval--------> [0,∞)

f(x)\geq 0

therefore

Statements

A) The range is the set of all real numbers

Is false

B) The domain is the set of all real numbers

Is true

C) The domain is the set of all real numbers greater than or equal to zero

Is false

D) The range is the set of all real numbers greater than or equal to zero

Is true


7 0
3 years ago
How can I solve (-12 =2 + k)
ZanzabumX [31]
You would want to go by reverse order of operations. This is a one step equation. You subtract 2 on both sides, in which you will get: -14 = k.
3 0
3 years ago
Read 2 more answers
Which expression is equivalent to -3(2m-1)-1
zloy xaker [14]

Answer:

-6m+2

Step-by-step explanation:

-6m+3-1

=-6m+2

Hope this helps

5 0
2 years ago
Other questions:
  • Calculate the total installment price the carrying charges in the number of months needed to save them money at the monthly rate
    11·1 answer
  • 9x+y=2<br> -4x-y=-17<br> solve the linear system using elimination
    12·2 answers
  • christopher divided 678 by a mystery number. in his quotient, 7 shifted 3 places to the left. express the mystery number in expo
    6·1 answer
  • The bird population in Louisiana is decreasing at a rate of 15% per day due to the oil spill. If there are 12,000 birds today, h
    14·1 answer
  • What is area computer screen with 21
    9·2 answers
  • Pls help ASAP because i'm am struggling i will mark brainliest if you r correct but you have to be for sure.
    14·2 answers
  • What radius of a circle is required to inscribe an equilateral triangle with an area of 270.633 cm2 and an altitude of 21.65 cm?
    6·2 answers
  • A six dice is rolled 150 times.Which of the following best describes how many times it is likely to land on a odd number
    15·1 answer
  • Help pls now points are 30
    13·1 answer
  • What’s the slope for (3,8)and (5,0)
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!