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The quadratic value function is y = -x² - 4x + 16

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

Let the function passes through the given points. (-1,-11) (2,-26) (-3,-31)

And , using the point (-1,-11) , we get

-11 = a(-1)² + b(-1) + c

-11 = a - b + c

Using the point (2,-26) , we get

-26 = a(2)² + b(2) + c

-26 = 4a + 2b + c

Using the point (-3,-31) , we get

-31 = a(-3)² + b(-3) + c

-31 = 9a - 3b + c

And , the three set of equations are

-11 = a - b + c

-26 = 4a + 2b + c

-31 = 9a - 3b + c

From the first equation, we can solve for c:

c = 11 - a + b

Substituting this expression for c into the other two equations, we get:

-26 = 4a + 2b + 11 - a + b

-31 = 9a - 3b + 11 - a + b

Simplifying these equations, we get:

-15 = 3a + 3b

-21 = 8a - 2b

Solving the first equation for b in terms of a, we get:

b = -5 - a

Substituting this expression for b into the second equation, we get:

-21 = 8a - 2(-5 - a)

Simplifying and solving for a, we get:

a = -1

Substituting this value of a into the equation for b that we found earlier, we get:

b = -5 - (-1) = -4

Finally, substituting these values of a and b into the equation for c that we found earlier, we get:

c = 11 - (-1) - (-4) = 16

Hence , the quadratic function that passes through the given points is given by y = -x² - 4x + 16

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Answer:

The answer is D

Step-by-step explanation:

Answer:

y = -3x + 6

Step-by-step explanation:

Equation of straight line is given by,

y = mx + b

m = slope of the line

b = y-intercept

From the graph attached,

m =

   =

   = -3

y intercept 'b' = 6

Therefore, equation of the line will be,

y = -3x + 6

Answer:

The amount of time is 8 years

Step-by-step explanation:

Simple interest refers to the interest produced by initial capital over a period of time. This does not accumulate to the capital to produce the interests of the following period, so the interest generated or paid in all periods is the same, while the interest rate and term dont vary.

The amount of interest paid or charged depends on three important amounts: Capital, rate and time. This is expressed by the following equation:

I = P * r * t

Where:

• I = interest.
• P = initial capital.
• r = interest rate in decimals (it is usually a given data in percentage, which you must divide by 100 to get the value in decimals).
• t = time in years.

In this case I has a value of $ 720, P has a value of $ 1000 and r of 9%, which making the conversion to decimal is 0.09

Replacing in the equation you get:

720=1000*0.09*t

Multiplying 1000 * 0.09 you get:

720=90*t

Dividing both sides by 90, in order to isolate t, you get:

8=t

Remembering that the value of t is expressed in years, this means that the amount of time is 8 years.

hope it helps.........