Answer:
[tex]f(x)=x^2+9x-10[/tex]
Step-by-step explanation:
Standard Form of Quadratic Function
The standard representation of a quadratic function is:
[tex]f(x)=ax^2+bx+c[/tex]
where a,b, and c are constants.
The factored form of a quadratic equation is:
[tex]f(x)=a(x-\alpha)(x-\beta)[/tex]
Where [tex]\alpha[/tex] and [tex]\beta[/tex] are the roots or zeros of f.
The question gives the zeros of the function: 1 and -10. This makes our function look like:
[tex]f(x)=a(x-1)[x-(-10)][/tex]
[tex]f(x)=a(x-1)(x+10)[/tex]
Operating:
[tex]f(x)=a(x^2+10x-x-10)[/tex]
Joining like terms:
[tex]f(x)=a(x^2+9x-10)[/tex]
Since we are not given any more conditions, we choose the value of a=1, thus. the required function is:
[tex]\boxed{f(x)=x^2+9x-10}[/tex]
