Question

Find the zeros of h(x)=2(x-11)^2 -8

Answer 1

To find the zeros, we must find when 0=2(x-11)²-8. Adding 8 to both sides using the additive property of equality, we have 8=2(x-11)². Similarly, we can divide 2 from both sides to get 4=(x-11)². Finding the square root of both sides, we have 2=|(x-11)| (note that we include absolute values because the square root must be ≥ 0. If x-11=|x-11|, then 2=x-11 and 13=x. If x-11=-|x-11|, we find that 2=-(x-11)=11-x, and 2+x=11, so x=9, making our zeros 13 and 9.

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Answer 2

`h(x)=2(x-11)^2-8\\\\\text{The zeros of the function }\ h(x):\\\\h(x)=0\iff2(x-11)^2-8=0\qquad\text{add 8 to both sides}\\\\2(x-11)^2=8\qquad\text{divide both sides by 2}\\\\(x-11)^2=4\iff x-11=\pm\sqrt4\\\\x-11=-2\ \vee\ x-11=2\qquad\text{add 11 to both sides}\\\\\boxed{x=9\ \vee\ x=13}`