Find the value of c in the quadratic equation, $y = a x ^ { 2 } + b x + c$ , if the parabola passes through the points (4, 4), (1, 8), and ( 3, 4).
A) c=8
B) c=-8
C) c=1
D) c=-1

Question

Quizplus · Accepted Answer

We can substitute the coordinates of each point into the equation and obtain a system of equations:
\begin{aligned} 4 &= 16a + 4b + c \ 8 &= a+b+c \ 4 &= 9a+3b+c \end{aligned}
Solving the system by elimination, we get:
$$a = -\frac{1}{2}, b = -\frac{9}{2}, c = -8.$$
Therefore, the value of c is -8, so the answer is choice B.

Find the Value of C in the Quadratic Equation y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c

Find the Value of C in the Quadratic Equation $y = a x ^ { 2 } + b x + c$