State all the transformations needed to transform f (x) = 3 (x-5) ^2 - 7 to have a vertex of (-2,4) and also be reflected on the x axis

shift 7 units to the left shift 11 units up multiply function by - 1

Transformed equation is: f (x) = - 3 (x + 2) + 4

Step-by-step explanation:

The vertex equation of a parabola is: f (x) = a (x - h) ² + k where

a is the vertical stretch (negative sign is a reflection over x-axis) (h, k) is the vertex

We are given f (x) = 3 (x - 5) ² - 7 - -> a = 3, (h, k) = (5, - 7)

→ We need to move the x-coordinate from 5 to - 2 (7 units left)

→ We need to move the y-coordinate from - 7 to 4 (11 units up)

→ To reflect over the x-axis, we need to make the a-value negative.