Write the equation of the parabola that has the same shape as the given parabola but with the given vertex.
-$f ( x ) = - 3 x ^ { 2 } ; ( 3 , - 4 )$
A) $f ( x ) = - 3 ( x + 4 ) ^ { 2 } + 3$
B) $f ( x ) = - 3 ( x - 4 ) ^ { 2 } + 3$
C) $f ( x ) = - 3 ( x - 3 ) ^ { 2 } - 4$
D) $f ( x ) = - 3 ( x + 3 ) ^ { 2 } - 4$

Question

Quizplus · Accepted Answer

The correct equation is $f(x) = -3(x - 3)^2 - 4$ because it reflects a parabola with the same shape as the given parabola $f(x) = -3x^2$, but shifted to have its vertex at the point (3, -4). The general form for a parabola's equation is $f(x) = a(x - h)^2 + k$, where (h, k) is the vertex.

Write the Equation of the Parabola That Has the Same f(x)=−3x2;(3,−4)f ( x ) = - 3 x ^ { 2 } ; ( 3 , - 4 )f(x)=−3x2;(3,−4)

Write the Equation of the Parabola That Has the Same $f ( x ) = - 3 x ^ { 2 } ; ( 3 , - 4 )$