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

1,645,493,059.35

step-by-step explanation: