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=?

Question
Performing transformations
asked 2021-01-15
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=?

Answers (1)

2021-01-16
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
\(g(x)=9(x-70^2-3\)
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Case: Dr. Jung’s Diamonds Selection
With Christmas coming, Dr. Jung became interested in buying diamonds for his wife. After perusing the Web, he learned about the “4Cs” of diamonds: cut, color, clarity, and carat. He knew his wife wanted round-cut earrings mounted in white gold settings, so he immediately narrowed his focus to evaluating color, clarity, and carat for that style earring.
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