Question 983097

Which value of C in the equation {{{y = x^2 - 5x + C}}} will provide zeros at {{{x[1] = -1}}} and{{{ x [2]= 6}}}? 

to find out, use zero product theorem

{{{(x-x[1])(x-x[2])=0}}}

{{{(x-(-1))(x-6)=0}}}

{{{(x+1)(x-6)=0}}}

{{{x^2-6x+x-6=0}}}

{{{x^2-5x-6=0}}} 


when you compare it to {{{y = x^2 - 5x + C}}}, you see that {{{highlight(C=-6)}}}

so, your equation is: 

{{{y = x^2 - 5x +(-6)}}}
or
{{{y = x^2 - 5x-6}}}

check it on a graph:


{{{ graph( 600, 600, -10, 10, -10, 10, x^2-5x-6) }}}