The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown. f(x) = 3(x2 – 8x) + 10 (-8/2)^2 = 16 What is the function written in vertex form? A. f(x) = 3(x + 4)2 – 6 B. f(x) = 3(x + 4)2 – 38 C. f(x) = 3(x – 4)2 – 6 D. f(x) = 3(x – 4)2 – 38

D

Step-by-step explanation:

Given

f(x) = 3x² - 24x + 10 ← factor out 3 from 3x² - 24x

     = 3(x² - 8x) + 10

Using the method of completing the square

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

f(x) = 3(x² + 2(- 4)x + 16 - 16) + 10

      = 3(x - 4)² - 48 + 10

      = 3(x - 4)² - 38 ← in vertex form → D

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!