Question

Write the function in vertex form.
y = 3x² - 8x + 13
The function is y=

Answer 1

y = 3(x -
`(4)/(3)` )² +
`(23)/(3)`

Explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

given

y = 3x² - 8x + 13

using the method of completing the square

the coefficient of the x² term must be 1 so divide first 2 terms by 3

y = 3(x² -
`(8)/(3)` x) + 13

add/subtract ( half the coefficient of the x- term )² to x² -
`(8)/(3)` x

y = 3(x² + 2(-
`(4)/(3)` )x +
`(16)/(9)` -
`(16)/(9)` ) + 13

= 3(x -
`(4)/(3)` )² + 3(-
`(16)/(9)` ) + 13

= 3(x -
`(4)/(3)` )² -
`(16)/(3)` +
`(39)/(3)`

= 3(x -
`(4)/(3)` )² +
`(23)/(3)` ← in vertex form