Find the quadratic polynomial $y = a x ^ { 2 } + b x + c$ whose graph passes through the points $( - 3,7 )$, $( - 2,1 )$, and $( 1,7 )$
A) $y = x ^ { 2 } + x$
B) $y = x ^ { 2 } - 4 x + 2$
C) $y = x ^ { 2 } + 2 x - 1$
D) $y = 2 x ^ { 2 } + 4$
E) $y = 2 x ^ { 2 } + 4 x + 1$

Question

Quizplus · Accepted Answer

Substitute the given points into the quadratic equation:
$$\begin{cases} 7 = 9c-3b+c \ 1 = 4c-2b+c \ 7 = c+b+c \end{cases}$$

This leads to the following system of equations:
$$\begin{cases} 11c - 3b = 7 \ 6c - 2b = 1 \ 2c + b = 7 \end{cases}$$

Solving this system of equations gives $c=2$ and $b=0$, which means that the quadratic polynomial is $y = 2x^2 + 4x + 1$. Therefore, the answer is E.

Find the Quadratic Polynomial y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c

Find the Quadratic Polynomial $y = a x ^ { 2 } + b x + c$