Find a quadratic function to model the values in the table. Predict the value of y for x = 6.

x y
1 2
0 2
3 -10

Question

Find a quadratic function to model the values in the table. Predict the value of y for x = 6.

x   y
1   2
0   2
3  -10

helder_edwin · Answer

the general quadratic function is
$$\large y=ax^2+bx+c $$
replace the three points u have and u will get three linear equations. then solve the system

anonymous · Answer

I tried that but i'm still not getting it =/

shamim · Answer

2=a+b+c
2=c
-10=9a+3b+c
solve this 3 equation for a,b,c

shamim · Answer

tell me the values of 
a,b ,c

whpalmer4 · Answer

Plugging in the values to get the equations:

$$y = ax^2+bx+c$$$$\begin{array}{cc}
x & y \\hline\ 0 & 2 \
 1 & 2 \
 3 & -10 \
\end{array}$$

$$2 = a (0)^2 + b(0) + c$$$$2 = c$$
$$2 = a(1)^2 + b(1) + c$$$$2 = a+b+c$$$$2 = a + b + 2$$$$0 = a+b$$

$$-10 = a(3)^2 + b(3) + c$$$$-10 = 9a + 3b + 2$$$$-12 = 9a+3b$$

So you have a system of 3 equations in 3 unknowns, although we've already found one of them, giving us a system of 2 equations in 2 unknowns:

$$~~~~~0 = ~~a+~~b$$$$-12 = 9a+3b$$
The first equation implies that $a = -b$, so we can substitute into the second equation;
$$-12 = 9(-b) + 3b$$What do you get for $b$ when you solve that equation?  From there, find the value of $a$ and write your full equation (remember that $c = 2$).  Use it to find the value of $y$ when $x=6$.