Using the completing-the-square method, rewrite f (x) = x2 + 10x + 7 in vertex form.

Question

Saul Barton

Mathematics

31 July, 05:40

Using the completing-the-square method, rewrite f (x) = x2 + 10x + 7 in vertex form.

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Gordon Flowers · Answer 1

f (x) = x² + 10x + 7

y = x² + 10x + 7

y - 7 = x² + 10x

y - 7 + 25 = x² + 10x + 25

y + 18 = x² + 5x + 5x + 25

y + 18 = x (x) + x (5) + 5 (x) + 5 (5)

y + 18 = x (x + 5) + 5 (x + 5)

y + 18 = (x + 5) (x + 5)

y + 18 = (x + 5) ²

y + 18 - 18 = (x + 5) ² - 18

y = (x + 5) ² - 18