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Create the equation of a cubic in standard form that has a double zero at -2, another zero at 4, and a y-intercept of 16,​

User Steveayre
by
8.4k points

1 Answer

1 vote

Answer:

f(x) =
(1)/(4) x³ - 3x - 4

Explanation:

Given that x = - 2 has multiplicity 2 and x = 4 are zeros then

(x + 2)² and (x - 4) are the factors of the polynomial and the polynomial is the product of the factors, thus

f(x) = a(x + 2)²(x - 4) ← a is a multiplier

To find a substitute (0, 16) into the equation

16 = a(4)(16), thus

64a = 16

a =
(16)/(64) =
(1)/(4)

f(x) =
(1)/(4)(x + 2)²(x - 4) ← expand factors

=
(1)/(4)(x² + 4x + 4)(x - 4)

=
(1)/(4)(x³ + 4x² + 4x - 4x² - 16x - 16)

=
(1)/(4)(x³- 12x - 16)

=
(1)/(4) x³ - 3x - 4

User Florian Straub
by
7.5k points

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