Question

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

Answer 1

we have

$f(x)=x^{2}-2x-3$

Find the roots

Equate the function to zero

$x^{2}-2x-3=0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^{2}-2x=3$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$x^{2}-2x+1=3+1$

$x^{2}-2x+1=4$

Rewrite as perfect squares

$(x-1)^{2}=4$

Square root both sides

$(x-1)=(+/-)2$

$x=1(+/-)2$

$x=1+2=3$

$x=1-2=-1$

therefore

the answer is

$x=3$

Answer 2

X^2 -2x -3 = 0

(x-3)(x+1)=0

x+1=0
x=-1

x-3=0
x = 3 

so the missing number is 3