Express the function y = 2x² + 8x + 1 in vertex form.

Solution:

Given, y = 2x² + 8x + 1

y = 2[ x² + 4x + 1/2]

y = 2[ x² + 4x + 2² - 2² +1/2]

y = 2[(x + 2)² -7/2]

y = 2(x + 2)² -7

2(x + 2)² = y + 7

(x + 2)² = 1/2(y + 7)

It is the required vertex form because it is of the form (x - h)² = 4a (y - k), a parabola whose vertex is at (h, k) = (-2, -7).

Express the function y = 2x² + 8x + 1 in vertex form.

Summary:

The function y = 2x² + 8x + 1 in vertex form is (x + 2)² = 1/2(y + 7).