Question

If the graph of the function y=x^2 is reflected over the x-axis , then translated two units left,write an equation to represent the function

Answer 1

Answer:  y = -(x + 2)²

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(bx - h)² + k    where

• a: vertical stretch (if negative it is a reflection across x-axis)
• b: horizontal stretch (if negative it is a reflection across y-axis)
• h: horizontal shift (negative is left and positive is right)
• k: vertical shift (negative is down and positive is up)
• (h, k): vertex of the function

Given: reflection over x-axis → a = -1,   two units left → c = -2

Input those values into the equation:  y = -(x - (-2))²

                                              simplify:   y = -(x + 2)²