Question

Given that f(x) is a cubic function with zeros at −5, 2, and 4, find an equation for f(x) given that f(−10)=−4.

Answer 1

f(x) = a(x+5)(x-2)(x-4)
f(-10) = a(-5)(-12)(-14) = -840a = -4
a = 1/210

f(x) = 1/210 (x+5)(x-2)(x-4)

Answer 2

ty!

Answer 3

A cubic function is a function of the form:

f ( x ) = a ^ 3 + b x ^ 2 + c x + d

You must find 4 coefficients:

a , b , c , and d

You now zero pionts:

x = - 5 , y = 0

x = 2 , y = 0

and

x = 4 , y = 0

You also know :

f ( - 10 ) = - 4

Now put this values in equation:

f ( x ) = a x ^ 3 + b x ^ 2 + c x + d


For x = - 5

a x ^ 3 + b x ^ 2 + c x + d = a * ( - 5 ) ^ 3 + b * ( - 5 ) ^ 2 + c * ( - 5 ) + d = 0


a * ( - 125 ) + b * 25 + c * ( - 5 ) + d = 0

- 125 a + 25 b - 5 c + d = 0


For x = 2

a x ^ 3 + b x ^ 2 + c x + d = a * 2 ^ 3 + b * 2 ^ 2 + c * 2 + d = 0

8 a + 4 b + 2 c + d = 0


For x = 4

a x ^ 3 + b x ^ 2 + c x + d = a * 4 ^ 3 + b * 4 ^ 2 + c * 4 + d = 0

64 a + 16 b + 4 c + d = 0


For x = - 10

a x ^ 3 + b x ^ 2 + c x + d = a * ( - 10 ) ^ 3 + b * ( - 10 ) ^ 2 + c * ( - 10 ) + d = - 4


a * ( - 1000 ) + b * 100 + c * ( - 10 ) + d = - 4

- 1000 a + 100 b - 10 c + d = - 4


Now you have system of 4 equaions with 4 unknow:

- 125 a + 25 b - 5 c + d = 0

8 a + 4 b + 2 c + d = 0

64 a + 16 b + 4 c + d = 0

- 1000 a + 100 b - 10 c + d = - 4


The soluitions are :

a = 1 / 210 , b = - 1 / 210 , c = - 11 / 105 , d = 4 / 21

Your equation:

f ( x ) = ( 1 / 210 ) x ^ 3 - ( 1 / 210 ) x ^ 2 - ( 11 / 105 ) x + 4 / 21

Or:

f ( x ) = ( 1 / 210 ) x ^ 3 - ( 1 / 210 ) x ^ 2 - 2 * 11 / 210 x + 40 / 210

f ( x ) = ( 1 / 210 ) ( x ^ 3 - x ^ 2 - 22 x + 40 )

Answer 4

that you!

Answer 5

thank*

Answer 6

how the hell do you do this.