Question

What is the x-intercept for y = (x – 1)^2 – 16? I already know the y-intercept is -16.

Answer 1

set equal to zero and solve
\[(x-1)^2-16=0\]
\[(x-1)^2=16\]
\[x-1=4\iff x=5\] or \[x-1=-4\iff x=-3\]
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Answer 2

\[(x-1)^2 - 16\]
\[(x-1)^2 = 16\]
\[x^2-2x+1 = 16\]
\[x^2-2x = 16-1\]
\[x^2 - 2x = 15\]
\[x(x-2)=15\]
so..\[x= 15 \]
and
\[x-2 = 15\]
\[x=15+2= 17\]

x=15 and x=17