Question 1169888


given:

{{{x[1]=x[2]=4}}}
{{{x[3]=0}}}
{{{x[4]=-1}}}
and it goes through the point ({{{5}}},{{{24}}})

{{{P(x)=a(x-x[1])(x-x[2])(x-x[3])(x-x[4])}}}
{{{P(x)=a(x-4)(x-4)(x-0)(x-(-1))}}}
{{{P(x)=a(x-4)(x-4)(x)(x+1)}}}
{{{P(x)=a(x^2 - 8x + 16)(x^2+x)}}}
{{{P(x)=a(x^4 - 7x^3 + 8x^2 + 16x)}}}.....use given point ({{{5}}},{{{24}}}) to calculate {{{a}}}

{{{24=a(5^4 - 7*5^3 + 8*5^2 + 16*5)}}}
{{{24=a(30)}}}
{{{a=24/30}}}
{{{a=4/5}}}

then
{{{P(x)=(4/5)(x^4 - 7x^3 + 8x^2 + 16x)}}}
{{{P(x)=(4x^4)/5 -(28x^3)/5 +(32x^2)/5 +(64x)/5}}}

{{{ graph( 600, 600, -10, 10, -10, 10, (4x^4)/5 -(28x^3)/5 +(32x^2)/5 +(64x)/5) }}}