Rewrite the equation in standard form. Determine whether the parabola is horizontal or vertical, the direction it opens,
and the vertex.
-$$y = - 3 x ^ { 2 } + 72 x - 441$$
A) $y = ( x + 12 ) ^ { 2 } - 9$
vertical, opens downward, vertex $( - 12 , - 9 )$
B) $y = ( x - 12 ) ^ { 2 } - 9$
vertical, opens upward, vertex $( 12 , - 9 )$
C) $y = ( x + 12 ) ^ { 2 } - 9$
vertical, opens upward, vertex $( - 12 , - 9 )$
D) $y = ( x - 12 ) ^ { 2 } - 9$
vertical, opens downward, vertex $( 12 , - 9 )$

Question

Quizplus · Accepted Answer

The given equation is in the form $y = ax^2 + bx + c$, which represents a vertical parabola. The negative coefficient of $x^2$ indicates it opens downward. Completing the square gives $y = -3(x - 12)^2 - 9$, making the vertex $(12, -9)$.

Rewrite the Equation in Standard Form y=−3x2+72x−441y = - 3 x ^ { 2 } + 72 x - 441y=−3x2+72x−441

Rewrite the Equation in Standard Form $y = - 3 x ^ { 2 } + 72 x - 441$