Let f(x)=x^2+10x+37 .what is the vertex form of f(x)? what is the minimum value of f(x)? enter your answers in the boxes. vertex form: f(x)= minimum value of f(x):

Thank you for the explanation!

To all future users: Here is simply the answers so you aren't confused.

Vertex form: f(x) = (x+5)²+12

Minimum value of f(x): 12

I hope that clears up any confusion...

Good luck! :)

We can go from standard from to vertex form using completing the square.

Standard form:
Vertex form: , where (h, k) is the vertex

Group the first two terms:





Now complete the square inside the parenthesis. Take half of the second term and square it, then add it and subtract it inside the parenthesis(so we don't change the function):

Half of 10 is 5, 5 squared is 25:



Factor the perfect square():



Simplify:



This is the function in vertex form.

The minimum value is the vertex, we can find this just by looking at our function in vertex form.

Vertex form: , where (h, k) is the vertex



'h' is -5 and 'k' is 12

So our minimum is: