Question

# Create a new function in the form y = a(x- h)^2 + k by performing the following transformations on f (x) = x^2

Performing transformations

Create a new function in the form $$y = a(x- h)^2 + k$$ by performing the following transformations on $$f (x) = x^2$$
Give the coordinates of the vertex for the new parabola.
h(x) is f (x) shifted right 3 units, stretched by a factor of 9, and shifted up by 7 units. $$h(x) = ?$$
Edit Coordinates of the vertex for the new parabola are:
$$x=?$$
$$y =?$$

2021-02-06

h(x) is f(x) shifted 3 units left. So, $$h(x)=f(x+3)$$
Then stretched by a factor of 2. So $$h(x)= 2f(x+3)$$
Reflected accross x axis. So, $$h(x) = -2f(x+3)$$
Then shifted up 7. $$h(x)= -2f(x+3)+7= -2(x+3)^2 + 7$$
Answer: $$h(x) = -2(x+3)^2 + 7$$
We compare h(x) with $$a(x-h)^2+k$$. So $$h=-3$$ and $$k=7$$.
Vertex$$=(h,k)=(-3,7)$$
Answer:Vertex$$= (-3,7)$$
$$h(x)=-2(x+3)^2+7$$