For the following exercises, use the given information about the polynomial graph to write the equation. Double zero at x = −3 and triple zero at x = 0. Passes through the point (1, 32).

iohanetc

iohanetc

Answered question

2021-03-08

For the following exercises, use the given information about the polynomial graph to write the equation. Double zero at x=3 and triple zero atx=0. Passes through the point (1, 32).

Answer & Explanation

BleabyinfibiaG

BleabyinfibiaG

Skilled2021-03-09Added 118 answers

Step 1 Data: x-intercept of multiplicity 2=3 x-intercept of multiplicity 3=0 Degree =5 Step 2 Since it is a fifth degree polynomial function with multiplicity of 2 and 3 for some zeros, its general equation becomes: f(x)=a(x+3)2(x0) Simplify: f(x)=ax3(x+3)2 In order to evaluate a, use the point on the graph (1,32), therefore substitute f(1)=32 in this equation: 32=a(1)3(1+3)2 Simplify: 32=a(1)(16)=16a Evaluate a: a=3216=2 This implies that the equation of the polynomial function is f(x)=2x3(x+3)2 Answer: The equation of the polynomial function is f(x)=2x3(x+3)2

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