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
Elodia [21]
2 years ago
6

1.) Determine the type of solutions for the function (Picture 1)

Mathematics
1 answer:
NNADVOKAT [17]2 years ago
7 0

Answer:

1) 2 nonreal complex roots

2) 1 Real Solution

3) 16

4) Reflected, narrower by a factor of 2/5, slides right 4 units and slides up 6 (units)

Step-by-step explanation:

1) The graph does not intercept the x-axis, therefore, there are no real solutions at the point y = 0

We get;

y = a·x² + b·x + c

At y = 6, x = -2

Therefore;

6 = a·(-2)² - 2·b + c = 4·a - 2·b + c

6 = 4·a - 2·b + c...(1)

At y = 8, x = 0

8 = a·(0)² + b·0 + c

∴ c = 8...(2)

Similarly, we have;

At y = 8, x = -4

8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8

16·a - 4·b = 0

∴ b = 16·a/4 = 4·a

b = 4·a...(3)

From equation (1), (2) and (3), we have;

6 = 4·a - 2·b + c

∴ 6 = b - 2·b + 8 = -b + 8

6 - 8 = -b

∴ -b = -2

b = 2

b = 4·a

∴ a = b/4 = 2/4 = 1/2

The equation is therefor;

y = (1/2)·x² + 2·x + 8

Solving we get;

x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))

x =( -2 ± √(-12))/1 = -2 ± √(-12)

Therefore, we have;

2 nonreal complex roots

2) Give that the graph of the function touches the x-axis once, we have;

1 Real Solution

3) The given function is f(x) = 2·x² + 8·x + 6

The general form of the quadratic function is f(x) = a·x² + b·x + c

Comparing, we have;

a = 2, b = 8, c = 6

The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;

D = 8² - 4 × 2 × 6 = 16

The discriminant of the function, D = 16

4.) The given function is g(x) = (-2/5)·(x - 4)² + 6

The parent function of a quadratic equation is y = x²

A vertical translation is given by the following equation;

y = f(x) + b

A horizontal to the right by 'a' translation is given by an equation of the form; y = f(x - a)

A vertical reflection is given by an equation of the form; y = -f(x) = -x²

A narrowing is given by an equation of the form; y = b·f(x), where b < 1

Therefore, the transformations of g(x) from the parent function are;

g(x) is a reflection of the parent function, with the graph of g(x) being narrower by 2/5 than the graph of the parent function. The graph of g(x) is shifted right by 4 units and is then slides up by 6 units.

You might be interested in
Need help with this math please.
Cerrena [4.2K]

Answer:

Do what it says and i'll give you the answer.

Step-by-step explanation:

1.  Because the slopes are negative recipricals of each other then these lines are perpendicular. y=x+7 (red line) y=-x+2 (green line) +graph%28+300%2C ...

2.

4 0
3 years ago
The area of a square piece of land is 784metersquared .What is the perimeter​
Marta_Voda [28]

Answer:

112 m

Step-by-step explanation:

The area (A) of a square is

A = s² ( s is the length of side )

Here A = 784 , then

s² = 784 ( take the square root of both sides )

s = \sqrt{784} = 28

Then

perimeter = 4s = 4 × 28 = 112 m

7 0
2 years ago
Read 2 more answers
A company employs two shifts of workers. Each shift produces a type of gasket where the thickness is the critical dimension. The
AURORKA [14]

Answer:

(−0.103371 ; 0.063371) ;

No ;

( -0.0463642, 0.0063642)

Step-by-step explanation:

Shift 1:

Sample size, n1 = 30

Mean, m1 = 10.53 mm ; Standard deviation, s1 = 0.14mm

Shift 2:

Sample size, n2 = 25

Mean, m2 = 10.55 ; Standard deviation, s2 = 0.17

Mean difference ; μ1 - μ2

Zcritical at 95% confidence interval = 1.96

Using the relation :

(m1 - m2) ± Zcritical * (s1²/n1 + s2²/n2)

(10.53-10.55) ± 1.96*sqrt(0.14^2/30 + 0.17^2/25)

Lower boundary :

-0.02 - 0.0833710 = −0.103371

Upper boundary :

-0.02 + 0.0833710 = 0.063371

(−0.103371 ; 0.063371)

B.)

We cannot conclude that gasket from shift 2 are on average wider Than gasket from shift 1, since the interval contains 0.

C.)

For sample size :

n1 = 300 ; n2 = 250

(10.53-10.55) ± 1.96*sqrt(0.14^2/300 + 0.17^2/250)

Lower boundary :

-0.02 - 0.0263642 = −0.0463642

Upper boundary :

-0.02 + 0.0263642 = 0.0063642

( -0.0463642, 0.0063642)

7 0
2 years ago
Find the total surface area of this triangular prism.
Irina18 [472]

Answer:

not sure but i think its 425 cm

Step-by-step explanation:

for the square i dont know

how its called in english the surface is 25×10= 250cm

and for the triangle its (25×14):2 = 175cm

so 175 + 250= 425cm

4 0
2 years ago
Bob left a tip of 15% for the lunch he just bought. If this lunch cost $24.40, how much of a tip did Bob leave?
Ber [7]

Answer:

i think 20.74

Step-by-step explanation:

I think that might be right because if you have 24.40 mines - 15% that is 20.74

3 0
2 years ago
Other questions:
  • What is additive identity
    8·2 answers
  • PLEASE HELP I NEED HELP ;(
    7·2 answers
  • 6. The cost to rent a room for a party is a one-time fee
    14·1 answer
  • Write an equation for a direct variation that includes the point (2,-6)
    10·2 answers
  • I need the answer to this please
    13·1 answer
  • A rectangle has a height of 4 and a width of x to the power of 2 plus 3x plus 2
    9·1 answer
  • Please HELP ITS A GRADE AND TIMED I WILL MARK BRAINLIEST
    9·1 answer
  • Is -14/3 greater than -4
    7·2 answers
  • 5.5 minutes = 330 seconds<br> A. True<br> B. False
    14·2 answers
  • Which is greater<br>1) 14/28 or 17/28 <br>2)26/35 or 26/38<br>3)18/18 or 12/12​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!