Answer:
f(x) = x² - 4x - 5
Explanation:
given the roots of a parabola x = a and x = b , then the factors are
(x - a) and (x - b)
the function is then the product of the roots , that is
f(x) = (x - a)(x - b)
from the graph the roots ( where graph crosses the x- axis ) are
x = - 1 and x = 5 , then corresponding factors are
(x - (- 1) ) and (x - 5) , that is (x + 1) and (x - 5) , then
f(x) = (x + 1)(x - 5) ← expand using FOIL
= x² - 5x + x - 5
f(x) = x² - 4x - 5