Solve Problems Using Systems in Three Variables
-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 $( - 2,4 ) , ( - 1 , - 4 )$, and $( 4,16 )$.
A) $\mathrm { a } = 2 ; \mathrm { b } = - 2 ; \mathrm { c } = - 8$
B) $\mathrm { a } = 2 ; \mathrm { b } = - 8 ; \mathrm { c } = - 2$
C) $a = - 2 ; b = - 2 ; c = - 8$
D) $\mathrm { a } = - 2 ; \mathrm { b } = - 8 ; \mathrm { c } = - 2$

Question

Quizplus · Accepted Answer

To find the values of $a$, $b$, and $c$, we substitute the given points into the quadratic equation $y = ax^2 + bx + c$ and solve the resulting system of equations. For $(-2, 4)$, we get $4 = 4a - 2b + c$. For $(-1, -4)$, we get $-4 = a - b + c$. For $(4, 16)$, we get $16 = 16a + 4b + c$. Solving this system yields $a = 2$, $b = -2$, and $c = -8$.

Solve Problems Using Systems in Three Variables -Find the Values a,ba , ba,b

Solve Problems Using Systems in Three Variables
-Find the Values $a , b$