Answer:
AB = [tex]\sqrt{18}[/tex] units
Step-by-step explanation:
The graph crosses the y- axis when x = 0
y = 0 + 0 - 3 = - 3 ⇒ A (0, - 3 )
The graph crosses the x- axis when y = 0 , that is
x² + 2x - 3 = 0
(x + 3)(x - 1) = 0 ← in factored form , then
x - 3 = 0 ⇒ x = - 3
x - 1 = 0 ⇒ x = 1
Then B (- 3, 0 )
Using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (0, - 3 ) and (x₂, y₂ ) = B (- 3, 0 )
AB = [tex]\sqrt{(-3-0)^2+(0-(-3))^2}[/tex]
= [tex]\sqrt{(-3)^2+(0+3)^2}[/tex]
= [tex]\sqrt{9+3^2}[/tex]
= [tex]\sqrt{9+9}[/tex]
= [tex]\sqrt{18}[/tex] ( ≈ 4.24 units ( to 2 dec. places ) )
