Question

If x2 + 8x + 15 = (X - h)? + k, what is the value of K?

Answer 1

The value of
`\( k \)` is
`\(-1\)`.

How did we get this value?

To find the value of
`\( k \)`, let's first complete the square on the quadratic expression
`\( x^2 + 8x + 15 \)`. The given quadratic expression can be factored as
`\( (x + 5)(x + 3) \)`. Therefore, we have:

`\[ x^2 + 8x + 15 = (x + 5)(x + 3) \]`

Now, let's express the right side in the form
`\((x - h)^2 + k\)`:

`\[ (x + 5)(x + 3) = (x + 4)^2 - 1 \]`

Comparing this with
`\( (x - h)^2 + k \)`, we can see that
`\( h = -4 \) and \( k = -1 \).` Therefore, the value of
`\( k \)` is
`\(-1\)`.