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
ANSWERED
asked 2021-02-05

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:
\(x=?\)
\(y =?\)

Answers (1)

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\(= (-3,7)\)
\(h(x)=-2(x+3)^2+7\)

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