Answer:
c=36
[tex]y = x^2 - 12x + 36[/tex]
Step-by-step explanation:
Given the equation [tex]y = x^2 - 12x + c[/tex]
We are to determine the value of c for which y has only one zero.
For the general form of a quadratic equation [tex]ax^2+bx+c=0[/tex], we can use the Discriminant to determine the nature of the roots.
If the Discriminant, [tex]D=b^2-4ac=0[/tex], then the equation has equal roots, i.e. one x-intercept.
[tex]y = x^2 - 12x + c\\a=1, b=-12, c=c\\D=(-12)^2-(4*1*c)=0\\144-4c=0\\-4c=-144\\c=36[/tex]
When c=36, the equation has only one root.
The equation therefore is: [tex]y = x^2 - 12x + 36[/tex]
