What is the vertex for the equation f (x) = 3 (x+4) ^2-5

F (x) = 3 (x + 4) ² - 5

f (x) = 3 (x + 4) (x + 4) - 5

f (x) = 3 (x² + 4x + 4x + 16) - 5

f (x) = 3 (x² + 8x + 16) - 5

f (x) = 3 (x²) + 3 (8x) + 3 (16) - 5

f (x) = 3x² + 24x + 48 - 5

f (x) = 3x² + 24x + 43

Take derivative ...

f' (x) = 3*2 * (x+4)

f' (x) is must be equal to 0.

6 * (x+4) = 0

x=-4

for x=-4; what is the y value?

for x=-4; f (x) = - 5

the vertex is (-4,-5)