Question

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

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