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

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asked Sep 17, 2023 206k views

1 Answer

ByteMe · Answer 1 · 2023-09-23T02:20:56+0000

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

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

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