Question

The vertex form of h(x) = x2 – 14x + 6 is h(x) = (x –
)2 –
.

Answer 1

To convert the quadratic function \( h(x) = x^2 - 14x + 6 \) into vertex form \( h(x) = (x - h)^2 + k \), we can complete the square.

1. Start with the original function:
\[
h(x) = x^2 - 14x + 6
\]

2. To complete the square, take the coefficient of \( x \) (which is \(-14\)), divide it by 2, and square it:
\[
\left(-\frac{14}{2}\right)^2 = (-7)^2 = 49
\]

3. Rewrite the quadratic by adding and subtracting \( 49 \):
\[
h(x) = (x^2 - 14x + 49) - 49 + 6
\]
\[
h(x) = (x - 7)^2 - 49 + 6
\]
\[
h(x) = (x - 7)^2 - 43
\]

Thus, in vertex form, we have:
\[
h(x) = (x - 7)^2 - 43
\]

So the values for the blanks are:
- \( (x - 7)^2 \)
- \( -43 \)

Final answer: \( h(x) = (x - 7)^2 - 43 \)