If the parabola 𝑦 = 𝑥 2 undergoes the transformations: reflected over the x-axis, translated 5 units left and 2 units down, and compressed vertically by a factor of 1 2 , what is its new equation?

Question

If the parabola 𝑦 = 𝑥 2 undergoes the following transformations: reflected over the x-axis, translated 5 units left and 2 units down, and compressed vertically by a factor of 1 2, what is its new equation?

Answer 1

Esther, if you want to move the parabola y= x² with vertex (0,0) 3 units left, it becomes y= (x + 3)² because now if x = -3, then y= 0. I hope it makes sense that if the new vertex is "3 to the left," then the entire parabola is "3 to the left."

If you want to move y= x² 5 units down, it becomes y= x² - 5

If you want a "steeper" or "faster" or "compressed " parabola by a factor of 4, then y= x² becomes y= 4x²

Ro "reflect over the x-axis," you want a "u-shape" facing down instead of a "u-shape," so y= x² becomes y = -x²

^{All of these work separately, so you can combine them to get your answer.}

^{Hope this helps, Andrew}