Question

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

Answer 1

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

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

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.