Question

Find the vertex of the graph of the function. f(x) = 3x^2 - 18x + 24

Answer 1

Explanation:

f(x) = 3x² - 18x + 24

f(x) = 3(x²-6x +8)

f(x) = 3 ((x² -6x+9) - 9) +8)

f(x) = 3 ( (x-3)²- 1 )

f(x) = 3(x-3)² - 3

note : the vertex of the graph of the function. f(x) = a(x-h)² + k is the point : (h;k)

in this exercice the vertex is : (3; -3 )

Answer 2

(3, - 3 )

Explanation:

Given a quadratic in standard form

f(x) = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

`x_(vertex)` = -
`(b)/(2a)`

f(x) = 3x² - 18x + 24 ← is in standard form

with a = 3, b = - 18

`x_(vertex)` = -
`(-18)/(6)` = 3

Substitute x = 3 into the equation for corresponding value of y

f(3) = 3(3)² - 18(3) + 24 = 27 - 54 + 24 = - 3

vertex = (3, - 3 )