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 $( - 1,10 ) , ( 2,1 )$, and $( 4 , - 15 )$.
A) a = 1; b = 9; c = -2
B) a = 1; b = -2; c = 9
C) a = -1; b = -2; c = 9
D) a = -1; b = 9; 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 $(-1, 10)$:$$10 = a(-1)^2 + b(-1) + c$$$$10 = a - b + c$$ (1)For $(2, 1)$:$$1 = a(2)^2 + b(2) + c$$$$1 = 4a + 2b + c$$ (2)For $(4, -15)$:$$-15 = a(4)^2 + b(4) + c$$$$-15 = 16a + 4b + c$$ (3)Solving this system of equations, we find:$$a = -1, b = -2, c = 9$$Thus, the correct answer is $a = -1$, $b = -2$, $c = 9$, which corresponds to choice C.

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