Write an equation for the quadratic function whose graph contains the given vertex and point.
-Vertex $( - 5 , - 5 )$, point $( - 2 , - 32 )$
A) $P ( x ) = 3 x ^ { 2 } + 30 x - 5$
B) $P ( x ) = - 3 x ^ { 2 } + 5 x - 5$
C) $P ( x ) = - 2 x ^ { 2 } + 30 x + 80$
D) $P ( x ) = - 3 x ^ { 2 } - 30 x - 80$

Question

Quizplus · Accepted Answer

The correct equation can be found using the vertex form of a quadratic equation, $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Given the vertex $(-5, -5)$, the equation starts as $y = a(x + 5)^2 - 5$. To find $a$, use the point $(-2, -32)$: $-32 = a(-2 + 5)^2 - 5$. Solving for $a$ gives $a = -3$, leading to the equation $y = -3(x + 5)^2 - 5$, which when expanded is $y = -3x^2 - 30x - 80$.

Write an Equation for the Quadratic Function Whose Graph Contains (−5,−5)( - 5 , - 5 )(−5,−5)

Write an Equation for the Quadratic Function Whose Graph Contains $( - 5 , - 5 )$