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Find the x-intercepts of the polynomial f(x) = -x^2+16

User Anthony Brien
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1 Answer

17 votes
17 votes

We want to find the x-intercepts of the polynomial


f(x)=\text{ -x}^2+16

this means, we want to find where this functon crosses the x axis. Recall that the x axis is the line y=0. So we want to solve this equation


0=\text{ -x}^2+16

if we multiply both sides by -1, we get


0=x^2\text{ -16}

on the right, we have a difference of squares, so we can factor it out as


0=(x+4)\cdot(x\text{ -4\rparen}

now, as this is a product of numbers, this means that each of the number could be 0. This means we have two different equations, which are


x+4=0

and


x\text{ -4=0}

on the first one, if we subtract 4 on both sides, we get


x=\text{ -4}

and on the second one, if we add 4 on both sides, we get


x=4

so the x-intercepts of the polynomial are x=4 and x= -4

User Magdaline
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