Question

Given ​ f(x)=x2+14x+40 ​.
Enter the quadratic function in vertex form in the box.

Answer 1

We are given the quadratic function:

$f(x)=x^{2}+14x+40$

The vertex form is given by:

$y=a(x-h)^{2}+k$

So we have to convert our quadratic form into this vertex form.

We can do so by applying factoring by completing the square method.

$f(x)=x^{2}+14x+40$

Step 1:

We take half of coefficient of x and add it to x.

Coefficient of x is 14, half of it is 7.

(x+7)²

Step 2:

Subtract square of 7 that is 49,

(x+7)²-49+40

(x+7)²-9

Answer:

The vertex form is given by:

$y=(x+7)^{2}-9$