Answer:
The vertex form is f(x) = 5 (x + 4 )²- 80
Step-by-step clarification:
The given function is f(x) = 40x + 5x²
Rewrite it in standard form f(x) = 5x² + 40x
Extract 5 from the first two terms f(x) = 5 (x² + 8 x)
Now, create a perfect square trinomial from this function,
By adding and subtracting '16' within the x² + 8x,[TAG_24]]
This gives us f(x) = 5 (x² + 8x + 16 - 16)
f(x) = 5 (x² + 8x + 16 )- 5 (16)
Thus, f(x) = 5 (x + 4 )²- 5 (16)
So, f(x) = 5 (x + 4 )²- 80
In general, the vertex form is expressed as f(x) = a (x - h )² + k, where (h, k) indicates the vertex.
For the function f(x) = 5 (x + 4 )²- 80, the vertex is located at ( -4, -80)
Therefore, the vertex form is f(x) = 5 (x + 4 )²- 80
