Question

Rewrite f(x) = x2 + 9x – 16 in vertex form. Identify the axis of symmetry, vertex, and whether the vertex is a maximum or minimum

help please

Answer 1

first coordinate of the vertex is always
\[-\frac{b}{2a}\]which is also the axis of symmetry
in your case it is
\[-\frac{9}{2\times 1}=-\frac{9}{2}\]

Answer 2

therefore to write it in "vertex form" you can write it as
\[x^2+9x-16=(x+\frac{9}{2})^2+k\]
to find \(k\) replace \(x\) in your original expression by \(\frac{9}{2}\)