Question

if a parabola is horizontally translated 15 units left, stretch by a factor of 20, vertically translated down 30 units and reflected in the x axis determine the equation of the parabola in vertex form

Answer 1

y' = a(x'- ((h-15)/20))² + -(k-30)

Explanation:

Vertex: (h,k)

horizontally translated 15 units left: (h-15 , k)

stretch by a factor of 20: ((h-15)/20 , k)

vertically translated down 30 units: ((h-15)/20 , k-30)

reflected in the x axis: ((h-15)/20 , -(k-30))

Vertex' (h' , k'): ((h-15)/20 , -(k-30))

Equation: y' = a(x'-h')² + k'

y' = a(x'- ((h-15)/20))² + -(k-30)

Answer 2

your normal parabola is y=x^2 but with translations you get the form y=a(x-h)^2+k. it is horizontally shifted by 15 so h=15, the stretch factor is 20 so a=20, it is translated down by 30 so k=-30, and it is reflected in the x axis so a is negative. your answer is y=-20(x-15)^2-30. DONT OPEN ANY SKETCHY LINKS!!!