Solve the problem.
-Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = 11 x ^ { 2 }$, but which has its vertex at $( 3,7 )$.
A) $f ( x ) = 11 ( x - 3 ) ^ { 2 } + 7$
B) $f ( x ) = 11 ( x + 3 ) ^ { 2 } + 7$
C) $f ( x ) = ( 11 x + 3 ) ^ { 2 } + 7$
D) $f ( x ) = 11 ( x + 7 ) ^ { 2 } + 3$

Question

Quizplus · Accepted Answer

The general equation for a vertical parabola is of the form:
$$f(x) = a(x-h)^2 + k$$
where (h,k) is the vertex of the parabola. 
Comparing this to the given function f(x) = 11x^2, we see that the vertex is (0,0).
To shift the vertex to (3,7), we need to subtract 3 from x and add 7 to the entire function. Thus, the equation becomes:
$$f(x) = 11(x-3)^2 + 7$$
which is choice A.

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