Question

Write the function in vertex form, and identify its vertex.
g(x) = 5x2 - 50x + 128

Answer 1

first coordinate of the vertex is always
\[-\frac{b}{2a}\] in your case you get
\[-\frac{-50}{2\times 5}=10\] so that is the first coordinate

Answer 2

well that was wrong wasn't it?

Answer 3

yeah

Answer 4

\[-\frac{b}{2a}=-\frac{-50}{2\times 10}=5\] my mistake

Answer 5

so first coordinate of the vertex is 5, to find the second
\g(x) = 5x2 - 50x + 128\]
\[g(5)=5\times 5^2-50\times 5+128=3\] so vertex is (5,3)

Answer 6

then to write in "vertex" form put
\[g(x)=5(x-5)^2+3\]