What is the polynomial equation for the points passing through (-2,0), (0,0), (1,-4), (2,0)?

1 Answer
Apr 6, 2016

Answer:

#f(x) = 4/3 (x^3-4x)#

Explanation:

First let defined a polynomial function in factor form as follow

#f(x) = a(x-b)(x-c)(x-d).....(x-z)#,

where #a# is a none zero leading coefficient and

#b, c, d.....z# are the#x# intercepts, of the function, which meant
#x= b, x= c, x= d...... x= z#

We are given the following x- intercepts

#x = -2 , y = 0#
#x= , y = 0 #
#x= 2, y= 0 #

And the value of
#x= 1, y = -4#

We can re-write the x-intercepts in the factor forms like this

# f(x) = (x)(x+2)(x-2) #

the general form is

#f(x) = a(x)(x-2)(x+2) #

#f(x) = a(x(x^2-4)#

#f(x) = a(x&3 - 4x)#

Since #x= 1, y = -4# , we can substitute that into the general form to solve for #a#

#f(1) = a(1^3 -4(1))#
#-4 = a(1-4)#
#-4 = -3a#
#a= 4/3#

So the general polynomial function that passing through the points
#(0,0),(2, 0), (-2,0), (1,-4) # is

#f(x) = 4/3 (x^3-4x)#

#f(x)= 4/3 x^3 - (16x) /3 #
@Vikki