Question 936323
given:
{{{x}}}| {{{-7}}}|{{{ -2}}}|{{{ 2}}}|{{{ 4}}}|
{{{y}}}| {{{42}}}| {{{7}}}| {{{15}}}| {{{31}}}|

{{{f(x)=(x-x[1])(x-x[2])(x-x[3])(x-x[4])}}}

{{{f(x)=(x+7)(x+2)(x-2)(x-4)}}}

{{{f(x)=(x^2+2x+7x+14)(x^2-4x-2x+8)}}}

{{{f(x)=(x^2+9x+14)(x^2-6x+8)}}}

{{{f(x)=x^4+9x^3+14x^2-6x^3-54x^2-84x+8x^2+72x+112}}}

{{{f(x)=x^4+3x^3-32x^2-12x+112}}}...a polynomial of minimum degree that fits the data


{{{drawing( 600, 600, -25, 25, -385, 385,locate(1.8,15,p(2,15)),locate(-2,7,p(-2,7)),circle(-2,7,.26),circle(1.8,15,.26),locate(4,31,p(4,31)),circle(4,31,.26),circle(-7.2,42,.26),locate(-7,42,p(-7,42)), graph( 600, 600, -25, 25, -385, 385, x^4+3x^3-32x^2-12x+112)) }}}