Answer:
vertex = (4, - 37 )
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
f(x) = 2x² - 16x - 5 ← factor 2 out of the first 2 terms
= 2(x² - 8x) - 5
using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² - 8x
f(x) = 2(x² + 2(- 4)x + 16 - 16) - 5
= 2(x - 4)² - 32 - 5
= 2(x - 4)² - 37 ← in vertex form
with vertex = (4, - 37 )
