Write the equation of the parabola that has the same shape as the given parabola but with the given vertex.
-$f ( x ) = - 3 x ^ { 2 } ; ( - 4 , - 7 )$
A) $f ( x ) = - 3 ( x + 4 ) ^ { 2 } - 7$
B) $f ( x ) = - 3 ( x + 7 ) ^ { 2 } - 4$
C) $f ( x ) = - 3 ( x + 4 ) ^ { 2 } + 7$
D) $f ( x ) = - 3 ( x - 7 ) ^ { 2 } - 4$

Question

Quizplus · Accepted Answer

The correct equation is $f(x) = -3(x + 4)^2 - 7$ because it reflects a parabola with vertex $(-4, -7)$, maintaining the same shape (direction and width) as the given parabola $f(x) = -3x^2$. The vertex form of a parabola is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Here, $h = -4$ and $k = -7$, leading to the equation $f(x) = -3(x + 4)^2 - 7$.

Write the Equation of the Parabola That Has the Same f(x)=−3x2;(−4,−7)f ( x ) = - 3 x ^ { 2 } ; ( - 4 , - 7 )f(x)=−3x2;(−4,−7)

Write the Equation of the Parabola That Has the Same $f ( x ) = - 3 x ^ { 2 } ; ( - 4 , - 7 )$