To express the function in vertex form, we can start by rewriting the quadratic function. The given function is:
f(x) = x² + 16x + 8
First, we need to complete the square. We take the coefficient of the x term, which is 16, divide it by 2 (getting 8), and then square it (resulting in 64).
We can rewrite the function as:
f(x) = (x² + 16x + 64) – 64 + 8
This simplifies to:
f(x) = (x + 8)² – 56
Now, we have the function in vertex form, which is:
f(x) = (x + 8)² – 56
In vertex form, the function clearly shows the vertex of the parabola at the point (-8, -56).