Question

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?

Answer 1

The value of k is 5.

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.

`1(x^(2) ?6x+9)-9+14`

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

`1(x?3)^(2) +5`

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

Therefore, the value of k is 5.