Write an equation for the quadratic function whose graph contains the given vertex and point.
-Vertex $( - 5,6 )$, point $( 0,56 )$ (Write your answer in vertex form.)
A) $\mathrm { P } ( \mathrm { x } ) = 2 ( \mathrm { x } + 5 ) ^ { 2 } + 6$
B) $P ( x ) = 2 ( x - 5 ) ^ { 2 } + 6$
C) $P ( x ) = \frac { 62 } { 25 } ( x + 5 ) ^ { 2 } - 6$
D) $P ( x ) = ( x + 5 ) ^ { 2 } + 31$

Question

Quizplus · Accepted Answer

The vertex form of a quadratic function is $P(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Given the vertex $(-5, 6)$, the equation starts as $P(x) = a(x + 5)^2 + 6$. To find $a$, use the point $(0, 56)$: $56 = a(0 + 5)^2 + 6$, solving for $a$ gives $a = 2$. Thus, the correct equation is $P(x) = 2(x + 5)^2 + 6$.

Write an Equation for the Quadratic Function Whose Graph Contains (−5,6)( - 5,6 )(−5,6)

Write an Equation for the Quadratic Function Whose Graph Contains $( - 5,6 )$