Question

Given ​ f(x)=x2+14x+40 ​.

Enter the quadratic function in vertex form in the box.
f(x)=

Answer 1

Answer: f(x) = (x+7)^2 -9

Explanation:

I know that this is late but hopefully it will help someone else.

Answer 2

we know that
the quadratic function in vertex form is--------------> y=a*(x-h)²+k

we have
f(x)=x²+14x+40
y=x²+14x+40

We can convert to vertex form by completing the square on the right hand side
y-40=x²+14x
y-40-49=x²+14x-49------> subtract 49 on BOTH sides to preserve the equality
y-40=(x²+14x+49)-49
y=(x²+14x+49)-49+40---------> y=(x+7)²-9

the answer is
the quadratic function in vertex form-----------> y=(x+7)²-9
the vertex is the point (-7,-9)