Write an equation for the quadratic function whose graph contains the given vertex and point.
-Vertex $( - 3,5 )$, point $( 3,113 )$
A) $P ( x ) = 3 x ^ { 2 } + 3 x + 5$
B) $P ( x ) = - 3 x ^ { 2 } + 18 x + 5$
C) $P ( x ) = 3 x ^ { 2 } - 18 x + 32$
D) $P ( x ) = 3 x ^ { 2 } + 18 x + 32$

Question

Quizplus · Accepted Answer

The correct answer is D because the equation of a quadratic function in vertex form is $P ( x ) = a ( x - h ) ^ { 2 } + k$, where $( h, k )$ is the vertex. Substituting the given vertex $( - 3,5 )$ into this equation, we get $P ( x ) = a ( x + 3 ) ^ { 2 } + 5$. To find the value of $a$, we can use the given point $( 3,113 )$. Substituting this point into the equation, we get $113 = a ( 3 + 3 ) ^ { 2 } + 5$. Solving for $a$, we get $a = 3$. Therefore, the equation of the quadratic function is $P ( x ) = 3 ( x + 3 ) ^ { 2 } + 5 = 3 x ^ { 2 } + 18 x + 32$.

Write an Equation for the Quadratic Function Whose Graph Contains (−3,5)( - 3,5 )(−3,5)

Write an Equation for the Quadratic Function Whose Graph Contains $( - 3,5 )$