Express The Function Y = 2x2 + 8x + 1 In Vertex Form. - Cuemath

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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).

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