Question

What is the vertex for the function f(x) = 3(x – 2)2 + 4?

Answer 1

Answer:

The vertex for the function f(x) = 3(x – 2)2 + 4 is at (2, 4).

Step-by-step explanation:

Find the vertex for f(x) = 3 (x - 2)^2 + 4

f(x) = 3 (x - 2)^2 + 4 can also be written as:

y = 3 (x - 2)^2 + 4

To find critical points, first compute f'(x):

d/(dx)(3 (x - 2)^2 + 4) = 6 (x - 2):

f'(x) = 6 (x - 2)

Solve 6 (x - 2) = 0

6x - 12 = 0

6x = 12

x = 2

iI you substitute x = 2 in 3 (x - 2)^2 + 4 then you get:

y = 3 (x - 2)^2 + 4

x = 2

y = 3 (2 - 2)^2 + 4

y = 3 (0)^2 + 4

y = 3 (0) + 4

y = 4

Answer: The vertex for the function f(x) = 3(x – 2)2 + 4 is at ( 2, 4 ).