Answer:
f(x)=x^2+9x-10
Step-by-step explanation:
Standard Form of Quadratic Function
The standard form 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, and a is constant.
We know the zeros of the function are 1 and -10. The function is:
[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 restrictions, we can choose the value of a=1, thus. the required function is:
[tex]\boxed{f(x)=x^2+9x-10}[/tex]
