Answer:
f(x) = (x + 1)(x - 4)
Explanation:
let f be the function
FACTORED FORM of f :
f(x) = a(x - p)(x - q)
Where p and q are the roots/zeros of f
and ‘a’ is a real number.
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Find p and q :
The roots of f are the x-coordinates where the graph crosses the x-axis, which can be read from the graph: x = -1 and x = 4 ⇒ p = -1 and q = 4.
then f(x) = a(x + 1)(x - 4)
Find ‘a’ :
f(3) = -4 ⇒ a((3) + 1)((3) - 4) = -4 ⇒ a(4)(-1) = -4 ⇒ -4a = -4 ⇒ a = 1
Therefore, f(x) = (x + 1)(x - 4)