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

1 Answer
Apr 6, 2016

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 thex 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
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