Answer:
Vertex form is f(x) = 5 (x + 4 )²- 80
Step-by-step explanation:
Given function is f(x) = 40x + 5x²
Re-write the function in standard form f(x) = 5x² + 40x
Factor out the first terms f(x) = 5 (x² + 8 x)
Now, form the function to perfect square trinomial,
Add and subtract '16' in function x² + 8 x to make this perfect square.
So, f(x) = 5 (x² + 8 x + 16 - 16)
f(x) = 5 (x² + 8 x + 16 )- 5 (16)
f(x) = 5 (x + 4 )²- 5 (16)
f(x) = 5 (x + 4 )²- 80
In general vertex form is f(x) = a (x - h )² + k , where (h , k) is vertex.
So, in function f(x) = 5 (x + 4 )²- 80, vertex is ( -4 , -80)
Hence, vertex form is f(x) = 5 (x + 4 )²- 80
