Question

Which values for h and k are used to write the function f of x = x squared + 12 x + 6 in vertex form?

h=6, k=36
h=−6, k=−36
h=6, k=30
h=−6, k=−30

Answer 1

To convert the quadratic function \( f(x) = x^2 + 12x + 6 \) into vertex form, we can use the method of completing the square.

1. Start with the original equation:
\[
f(x) = x^2 + 12x + 6
\]

2. Focus on the quadratic and linear terms \( x^2 + 12x \). To complete the square, take half of the coefficient of \( x \) (which is 12), square it, and add and subtract this value inside the function. Half of 12 is 6, and \( 6^2 = 36 \).

3. Rewrite the function:
\[
f(x) = (x^2 + 12x + 36) - 36 + 6
\]
\[
f(x) = (x + 6)^2 - 30
\]

Now, we have the function in vertex form \( f(x) = (x + 6)^2 - 30 \).

From this, we can see that:
- \( h = -6 \) (since the vertex form is \( (x - h)^2 + k \))
- \( k = -30 \)

Thus, the values for \( h \) and \( k \) are:

\[
\text{h} = -6, \text{ k} = -30
\]

So the correct answer is:
**h = -6, k = -30**.