Question

Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form.

A) f(x) = (x − 8)^2


B) f(x) = (x − 4)^2 − 13


C) f(x) = (x − 4)^2 + 3


D) f(x) = (x − 4)^2 + 16

Answer 1

B

Explanation:

f(x) =
`x^(2) -8x+3`

=> f(x)=
`x^(2) -2(x)(4)+4^(2)-4^(2)+3`

=> f(x) =
`(x-4)^(2)-4^(2)+3`

=> f(x) =
`(x-4)^(2)-16+3`

=> f(x) =
`(x-4)^(2)-13`

Answer 2

f(x) = (x - 4)² - 13

Explanation:

f(x) = x² − 8x + 3

x² − 8x + 3 = 0

x² - 8x = -3

x² - 8x + 4² = -3 + 4²

x² - 8x + 4² = -3 + 16

x² - 8x + 4² = 13

(x - 4)² = 13

(x - 4)² - 13 = 0

The vertex form of a quadriatic function f(x) = x2 − 8x + 3 is;

f(x) = (x - 4)² - 13