Question

What is the equation for the function shown in FACTORED FORM?

Answer 1

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)