Question

Write the function in vertex form and identify its vertex.
g(x) = x2 - 10x + 11

Answer 1

same idea as the last one. lets see if i can do it without making a mistake

Answer 2

\[-\frac{b}{2a}=\frac{10}{2}=5\] and
\[g(5)=5^2-10\times 5 +11=25-50+11=-25+11=-14\] so vertex is
\[(5,-14)\] and vertex form will be
\[g(x)=(x-5)^2-14\]

Answer 3

you can check that this is correct by multiplying out
\[(x-5)^2-14\] and see that you get
\[x^2-10x+11\]

Answer 4

got it!

Answer 5

always works like this.
you can also "complete the square" if you like, but it is unnecessary