Question

What is the vertex of f(x) = | 8x + 8| - 3?

Answer 1

Answer:

(-1, -3)

Step-by-step explanation:

Vertex of y = |x| have the coordinates (0, 0).

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units to the left

f(x - n) - shift the graph n units to the right

nf(x) - stretches/shrinks vertically

f(nx) - stretches/shrinks horizontally

We have

f(x) = |8x + 8| - 3 = |8(x + 1)| - 3 = |8| · |x+1| - 3 = 8|x + 1| - 3

g(x) = |x| → f(x) = 8g(x + 1) - 3

vertically streched by 8      (0, 8 · 0) → (0, 0)

shifted 1 unit to the left    (0 - 1, 0) → (-1, 0)

shifted 3 units down       (-1, 0 - 3) → (-1, -3)