Solve the problem.
-Find the values of $a , b$, and $c$ such that the graph of the quadratic equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 1 , - 5 ) , ( 2,13 )$, and $( 3,23 )$.
A) $\mathrm { a } = 1 ; \mathrm { b } = 5 ; \mathrm { c } = - 1$
B) $\mathrm { a } = 1 ; \mathrm { b } = - 1 ; \mathrm { c } = 5$
C) $a = - 1 ; b = 5 ; c = - 1$
D) $a = - 1 ; b = - 1 ; c = 5$

Question

Quizplus · Accepted Answer

Substitute the given three points into the equation of the quadratic: $\begin{aligned} y & = a x ^ { 2 } + b x + c \ - 5 & = a ( - 1 ) ^ { 2 } + b ( - 1 ) + c \ 13 & = a ( 2 ) ^ { 2 } + b ( 2 ) + c \ 23 & = a ( 3 ) ^ { 2 } + b ( 3 ) + c \end{aligned}$
which simplifies to:

$\begin{aligned} - a + b - c & = - 5 \ 4 a + 2 b + c & = 13 \ 9 a + 3 b + c & = 23 \end{aligned}$

Solving this system of equations for $a$, $b$, and $c$, we get $a = 1$, $b = 5$, and $c = -1$. Therefore, the answer is A.

Solve the Problem a,ba , ba,b , And ccc Such That the Graph of the Quadratic Equation

Solve the Problem $a , b$ , And $c$ Such That the Graph of the Quadratic Equation