# 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

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.
g(x) is f (x) shifted right 7 units, stretched by a factor of 9, and then shifted down by 3 units. g(x) = ?
Coordinates of the vertex for the new parabola are:
x=?
y=?

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bahaistag

Given information:
The given function is $$f(x)=x^2$$.
Concept Used:
If a is positve real number, then the graph of $$f(x-a)$$ is the graph of $$y=f(x)$$ shifted to the right a units.
If $$a>1$$, the graph of $$y=cf(x)$$ is the graph of $$y =f(x)$$ stretched vertically by a.
If a is positve real number, then the graph of $$f(x)-a$$ is the graph of $$y=f(x)$$ shifted downward a units.
Calculation:
First, we have to shift the graph to the right by 7 units.
$$f(x-7)=(x-7)^2$$
Now, stretched the graph by a factor of 9 units.
$$9f(x-7)=9(x-7)^2$$
Now, shift the above graph downward by 3 units.
$$9f(x-7)-3=9(x-7)^2-3$$
Compare the new equation with the equation $$y=a(x-h)^2+k$$, we get
$$h=7$$ and $$k=-3$$
Final Statement:
The new coordinates of the vertex for the new parabola function is (7,-3)
The new function is
$$g(x)=9(x-70^2-3)$$