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

Chesley

Chesley

Answered question

2021-02-05

Create a new function in the form y=a(xh)2+k by performing the following transformations on f(x)=x2
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=?

Answer & Explanation

likvau

likvau

Skilled2021-02-06Added 75 answers

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(xh)2+k. So h=3 and k=7.
Vertex=(h,k)=(3,7)
Answer:Vertex=(3,7)
h(x)=2(x+3)2+7

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