Question

What are the coordinates of the vertex for f(x) = x2 + 4x + 10?

Answer 1

Answer: (-2,6)

Step-by-step explanation: I took the test on FLVS

Answer 2

You have to complete the square to get it into vertex form.  Do this by setting the function equal to zero and at the same time moving the constant over to the other side of the equals sign so you have this: $x^{2} +4x=-10$.  Now we can complete the square on the polynomial by taking half the linear term, squaring it, and adding it to both sides.  Our linear term is 4. Half of 4 is 2, and 2 squared is 4, so we add 4 to both sides: $( x^{2} +4x+4)=-10+4$ and simplify to get $( x^{2} +4x+4)=-6$.  In this process we have created a perfect square binomial on the left, which happens to be $(x+2) ^{2}=-6$.  Now move the -6 back over by addition to get $(x+2) ^{2} +6=y$.  The vertex is found at (-2, 6), the third choice down.