Question

Using the graph of f(x)=x^2 as a guide, describe the transformations, and then graph each function.

h(x)= -1/2x^2 +2

I can graph, I just need the rest.

Answer 1

multiplying the whole function by -1 reflects the function across the x axis
so f(x) to -f(x) would be a reflection across the x axis


multiplying the whole function by a fraction is a vertical transformation, if you multiply by a value x, such that 0<x<1, then it is a vertical shrink, if x>1, then it is a vertical stretch
so like f(x) to 2f(x) is a vertical stretch by a factor of 2

adding a value to the whole function moves it up by that number



ok

so
`f(x)=(-1)((1)/(2))(x^2)+2`
we have multiplied the whole thing by -1 and 1/2 and then added 2 to the whole function

that is a reflection across the x axis, a vertical shrink by a factor of 1/2, and translated up by 2 units in that order