Quadratic Translations

Question

how do you solve the question if the parent parabola is y=x², has been reflected in the x-axis, vertically stretched by a factor of 5, translated 2 units to the left and 1 unit up. and then change it to vertex form?

Answer 1

to be reflected over the x axis, y becomes -y

-y = x^2

y = -x^2

stretched by a factor of 5

y = -5x^2

2 units to the left

y = -5(x+5)^2

up 1

y = -5(x+5)^2 +1

vertex form

y =a(x-h)^2 + k where vertex = (h,k) = (-5, 1)

y = -5(x - -5)^2 + 1