Question 1186730

Second-degree, with zeros of {{{x[1]=-4}}} and {{{x[2]=6}}}, and goes

 to −∞ as x→−∞.

{{{p(x) =(x-x[1])(x-x[2])}}}

{{{p(x) =(x-(-4))(x-6)}}}

{{{p(x) =(x+4)(x-6)}}}

{{{p(x) =x^2 - 2x - 24}}}

for the condition that {{{y}}}→ −∞ as {{{x}}}→ −∞

we require the coefficient of x^2  to be negative

{{{p(x) =-(x^2 - 2x - 24)}}}

{{{p(x) =-x^2 + 2x + 24}}} is the required polynomial


{{{ graph( 600, 600, -10, 10, -10, 30, -x^2 +2x+24) }}}