Write a quadratic function in a standard form whose graph passes through (−8, 0), (1, 0), and (2, 30).

f (x) =

The equation is y = 5*x^2 + 65*x - 70

Step-by-step explanation:

We have 3 points for our equation, the if our equation has the shape

y = ax^2 + bx + c

we have the 3 equations:

0 = a(-8)^2 + b*-8 + c = a*64 - b*8 + c

0 = a(1)^2 + b*1 + c = a + b + c

30 = a2^2 + b*2 + c = a*4 + b*2 + c

Now we have 3 equations and 3 variables, let's solve the system.

64*a - 8 *b + c = 0

a + b + c = 0

4*a + 2*b + c = 30

Let's isolate one of the variables, i chose to isolate c in the second equation and get

c = -a - b

now we can replace it in the other two equations:

64*a - 8*b + (-a - b) = 63*a - 9*b = 0

4*a + 2*b + (-a - b) = -3*a + b  = 30

now we can isolate b in the second equation and get:

b = 30 + 3*a

and we replace it in the other eqution:

63*a - 9*(30 + 3*a) = 0

63*a  - 180 - 27*a = 0

(63 - 27)*a - 180 = 0

36*a = 180

a = 180/36 = 5

Now we can find the value of b:

b = 30 + 3*a = 30 + 3*5 = 30 + 35 = 65

Now we can find the value of c.

c = -a - b = -5 - 65 = 70

The equation is:

y = 5*x^2 + 65*x - 70

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get

"exterior angles = 360 / number of sides.

60 = 360 / sides

sides = 360 / 60

sides = 6"