We want to find the x-intercepts of the polynomial
[tex]f(x)=\text{ -x}^2+16[/tex]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
[tex]0=\text{ -x}^2+16[/tex]if we multiply both sides by -1, we get
[tex]0=x^2\text{ -16}[/tex]on the right, we have a difference of squares, so we can factor it out as
[tex]0=(x+4)\cdot(x\text{ -4\rparen}[/tex]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
[tex]x+4=0[/tex]and
[tex]x\text{ -4=0}[/tex]on the first one, if we subtract 4 on both sides, we get
[tex]x=\text{ -4}[/tex]and on the second one, if we add 4 on both sides, we get
[tex]x=4[/tex]so the x-intercepts of the polynomial are x=4 and x= -4
