Answer:
The required form is [tex]y=(x+7)^2-9[/tex].
Step-by-step explanation:
Consider the provided quadratic function.
[tex]y=x^2 + 14x + 40[/tex]
We need to put the equation into the form [tex]y = (x - h )^2 + k[/tex]
Add and subtract 49 in order to make the above function a perfect square.
[tex]y=x^2 + 14x+49-49 + 40[/tex]
[tex]y=x^2 + 14x+7^2-49 + 40[/tex]
[tex]y=(x+7)^2-49 + 40[/tex]
[tex]y=(x+7)^2-9[/tex]
Hence, the required form is [tex]y=(x+7)^2-9[/tex].
