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

Question

Lilah Solomon

Mathematics

1 May, 16:57

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

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Answers (1)

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Gamble · 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