Willie changes the quadratic function f(x)=x2? 6x+14 to vertex form f(x)=a(x? h)2+k. if willie does this correctly, what is the value of k?

The value of k is 5.

Step-by-step explanation:

Since we know we can convert function's quadratic form to vertex form by completing the square.

f(x)=x2?6x+14

We will add and subtract 9 to our equation in order to complete the square.

Upon completing the square and combining like terms we will get,

Upon comparing Willie's vertex form with our expression we can see that k is 5.

Therefore, the value of k is 5.

dwe

step-by-step explanation:

ewd

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: