Find the vertex.
f(x) = 6(x + 5)2-10

Vertex: (-5, -10)

Step-by-step explanation:

Parent graph: f(x) = a(bx - c)ⁿ + d

a = vertical shrink/stretch

b = horizontal shrink/stretch

c = horizontal movement left/right

d = vertical movement up/down

(c, d) is vertex

Step 1: Define function

f(x) = 6(x + 5)² - 10

Step 2: Define transformation

a = 6, Vertical stretch of 6

b = 1, No horizontal transformation

c = -5, move left 5 units.

d = -10, move down 5 units.

(-5, -10), vertex

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

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