Find a quadratic model for the sequence with the indicated terms. $a _ { 0 } = - 3 , a _ { 2 } = - 7 , a _ { 6 } = - 57$ A)an = $\frac { 3 } { 2 }$ n² - $\frac { 7 } { 4 }$ n - 3 B)an = -3n² + $\frac { 3 } { 2 }$ n - $\frac { 7 } { 4 }$ C)an = $- \frac { 7 } { 4 }$ n² + $\frac { 3 } { 2 }$ n - 3 D)an = - $\frac { 7 } { 4 }$ n² + $\frac { 3 } { 2 }$ n + 3 E)an = 3n² + $\frac { 3 } { 2 }$ n - $\frac { 7 } { 4 }$

Question

Quizplus · Accepted Answer

We know that the general form of a quadratic equation is $an^2+bn+c$. We can plug in the given information to form a system of three equations:

$4a-2b+c=-3$
$16a-4b+c=-7$
$36a-6b+c=-57$

Solving this system, we find $a=-\frac{7}{4}$, $b=\frac{3}{2}$, and $c=-3$. Thus, the quadratic model is: 
$$an^2+bn+c=-\frac{7}{4}n^2+\frac{3}{2}n-3$$

The correct choice is $\boxed{	extbf{(C)}}.$

Find a Quadratic Model for the Sequence with the Indicated a0=−3,a2=−7,a6=−57a _ { 0 } = - 3 , a _ { 2 } = - 7 , a _ { 6 } = - 57a0​=−3,a2​=−7,a6​=−57

Find a Quadratic Model for the Sequence with the Indicated $a _ { 0 } = - 3 , a _ { 2 } = - 7 , a _ { 6 } = - 57$