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 $( - 3,5 ) , ( 1,1 )$, and $( 2 , - 5 )$.
A) $a = 1 ; b = - 3 ; c = 5$
B) $a = 1 ; b = 5 ; c = - 3$
C) $a = - 1 ; b = 5 ; c = - 3$
D) $a = - 1 ; b = - 3 ; c = 5$

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 $(-3, 5)$:$$5 = a(-3)^2 + b(-3) + c$$$$5 = 9a - 3b + c$$For $(1, 1)$:$$1 = a(1)^2 + b(1) + c$$$$1 = a + b + c$$For $(2, -5)$:$$-5 = a(2)^2 + b(2) + c$$$$-5 = 4a + 2b + c$$Solving this system of equations yields $a = -1$, $b = -3$, and $c = 5$, which corresponds to choice D.

Solve the Problem aaa bbb , 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