SOLUTION: 1. describe the transformation of g(x)=-(x-4)^2+1 relative to f(x)=x^2 2.for polynomial function f(x)=x^4-3x^3-3x^3-3x^2+11x-6, list ral zero and multiplicity; find y-intercept

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Question 60865: 1. describe the transformation of g(x)=-(x-4)^2+1 relative to f(x)=x^2
2.for polynomial function f(x)=x^4-3x^3-3x^3-3x^2+11x-6, list ral zero and multiplicity; find y-intercept and some points.
3. Determine if -1 is a zero of P(x)=x^21-2x^18+5x^12+7x^2-3x+2
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
1. describe the transformation of g(x)=-(x-4)^2+1 relative to f(x)=x^2
Start by looking at "x" on the right side:
The -4 moves f(x)=x^2 four to the right.
The negative sign reflects the curve in the y- axis.
The +1 increases all y-values by 1 or raised the curve 1.
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2.for polynomial function f(x)=x^4-3x^3-3x^2+11x-6, list ral zero and multiplicity; find y-intercept and some points.
The coefficients add up to zero so x=1 is a zero.
Dividing by x-1 you get:
x^3-2x^2-5x+6
These coefficients add up to zero so x=1 is again a zero.
Dividing by x-1 you get:
x^2-x-6
This factors as:
(x-3)(x+2)=0
x=3 or x=-2
ZEROES:
x=1; multiplicity 2
x=3; multiplicity 1
x=-2; multiplicity 1
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3. Determine if -1 is a zero of P(x)=x^21-2x^18+5x^12+7x^2-3x+2
f(-1)=1-2(1)+5(1)+7(1)-3(-1)+2
f(-1) is not zero so -1 is not a zero.
Cheers,
Stan H.