Question

look at this table:

x	y
3	-54
4	-96
5	-150
6	-216

write a linear ($y = mx + b$), quadratic ($y = ax^2$), or exponential ($y = a(b)^x$) function that models the data.
$y = \square$

Explanation:

Step1: Test quadratic model form

We assume the function is $y=ax^2$. Substitute $x=2, y=-24$ into the equation:
$$-24 = a(2)^2$$

Step2: Solve for coefficient $a$

Calculate $2^2=4$, then rearrange to solve for $a$:
$$a = \frac{-24}{4} = -6$$

Step3: Verify with other $x$ values

Check $x=3$: $y=-6(3)^2=-6\times9=-54$, which matches the table.
Check $x=4$: $y=-6(4)^2=-6\times16=-96$, which matches the table.
Check $x=5$: $y=-6(5)^2=-6\times25=-150$, which matches the table.
Check $x=6$: $y=-6(6)^2=-6\times36=-216$, which matches the table.

Answer:

$y = -6x^2$