Determine the number of x-intercepts that appear on a graph of each function. f (x) = (x - 6)2(x + 2)2

Mathematics

2 answers:

Minchanka [31]3 years ago

7 0

Answer:

Step-by-step explanation:

Tpy6a [65]3 years ago

6 0

The number of x-intercepts that appear on the graph of the function
f(x)=(x-6)^2(x+2)^2 is two (2): x=6 (multiplicity 2) and x=-2 (multiplicity 2)

Solution
x-intercepts:
f(x)=0→(x-6)^2 (x+2)^2 =0

Using that: If a . b =0→a=0 or b=0; with a=(x-6)^2 and b=(x+2)^2

(x-6)^2=0
Solving for x. Square root both sides of the equation:
sqrt[ (x-6)^2] = sqrt(0)→x-6=0
Adding 6 both sides of the equation:
x-6+6=0+6→x=6 Multiplicity 2

(x+2)^2=0
Solving for x. Square root both sides of the equation:
sqrt[ (x+2)^2] = sqrt(0)→x+2=0
Subtracting 2 both sides of the equation:
x+2-2=0-2→x=-2 Multiplicity 2

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Step-by-step explanation:

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