the roots of the function f(x) = x² - 2x - 3 are shown. what is the missing number? x = -1 and x =

Explanation:

Step1: Factor the quadratic function

We factor $x^{2}-2x - 3$. We need two numbers that multiply to $-3$ and add up to $-2$. The numbers are $-3$ and $1$, so $x^{2}-2x - 3=(x - 3)(x+1)$.

Step2: Find the roots

Set $(x - 3)(x + 1)=0$. By the zero - product property, if $ab = 0$, then $a=0$ or $b = 0$. So $x-3=0$ gives $x = 3$ and $x + 1=0$ gives $x=-1$.

Answer:

$3$