Question

look at this table:

x	y
-9	-729
-8	-576
-7	-441
-6	-324
-5	-225

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 relationship

Check if $y = ax^2$ fits. Substitute $x=-9, y=-729$:
$$-729 = a(-9)^2$$
$$-729 = 81a$$

Step2: Solve for coefficient $a$

Calculate $a$ by division:
$$a = \frac{-729}{81} = -9$$

Step3: Verify with other points

Test $x=-8$: $y = -9(-8)^2 = -9(64) = -576$, which matches. Test $x=-7$: $y = -9(-7)^2 = -9(49) = -441$, which matches. All points fit.

Answer:

$y = -9x^2$