Question

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

Explanation:

Step1: Factor the quadratic function

To find the roots of \( f(x) = x^2 - 2x - 3 \), we factor the quadratic. We need two numbers that multiply to \(-3\) and add to \(-2\). The numbers are \(-3\) and \(1\), so we can factor as:
\( f(x) = (x - 3)(x + 1) \)

Step2: Set each factor to zero

To find the roots, we set each factor equal to zero:

• For \( x + 1 = 0 \), we get \( x = -1 \) (which is given).
• For \( x - 3 = 0 \), we get \( x = 3 \).

Answer:

\( 3 \)