Answer: 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
