Question

look at this table:

x	y
4	-80
5	-125
6	-180
7	-245

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 $x=3, y=-45$ into the equation:
$$-45 = a(3)^2$$

Step2: Solve for coefficient $a$

Calculate $3^2=9$, then solve for $a$:
$$a = \frac{-45}{9} = -5$$

Step3: Verify with other points

Check $x=4$: $y=-5(4)^2=-5\times16=-80$, which matches the table.
Check $x=5$: $y=-5(5)^2=-5\times25=-125$, which matches the table.
Check $x=6$: $y=-5(6)^2=-5\times36=-180$, which matches the table.
Check $x=7$: $y=-5(7)^2=-5\times49=-245$, which matches the table.

Answer:

$y = -5x^2$