Find an expression for a cubic function f if f(1) = 24 and
f(−5) = f(0) = f(2) = 0.
1) f(x) =
f(x) = Ax(x+5)(x-2)
24 = -6A
f(x) = -4x(x+5)(x-2)
-5, 0, and 2 are zeros.
That means that (x + 5), (x - 0) and (x - 2) are factors.
So f(x) = a(x + 5)(x)(x - 2) for some real number a.
Now plug in x = 1 and f(x) = 24 to solve for a.
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Verified answer
f(x) = Ax(x+5)(x-2)
24 = -6A
f(x) = -4x(x+5)(x-2)
-5, 0, and 2 are zeros.
That means that (x + 5), (x - 0) and (x - 2) are factors.
So f(x) = a(x + 5)(x)(x - 2) for some real number a.
Now plug in x = 1 and f(x) = 24 to solve for a.