Find the equation of the parabola passing through the given points. $( - 2,6 ) , ( 1,12 )$, and $( 2,18 )$
A) $\quad y = - 2 x ^ { 2 } + 3 x + 20$
B) $y = x ^ { 2 } + 3 x + 8$
C) $y = 3 x + 3$
D) $\quad y = x ^ { 2 } - 3 x + 8$
E) none of these

Question

Quizplus · Accepted Answer

We can use the general equation of a parabola, $y=ax^2+bx+c$, and substitute the coordinates of the given points to get a system of equations:
$$\begin{cases} 6=4a-2b+c \ 12=a+b+c \ 18=4a+2b+c \end{cases}$$
Solving this system, we get $a=1$, $b=3$, and $c=8$, so the equation of the parabola is $y=x^2+3x+8$. Therefore, the answer is B.

Find the Equation of the Parabola Passing Through the Given (−2,6),(1,12)( - 2,6 ) , ( 1,12 )(−2,6),(1,12)

Find the Equation of the Parabola Passing Through the Given $( - 2,6 ) , ( 1,12 )$