CPM Homework Help : APCALC Problem 2-68

If you plot the finite differences of a parabola, the result will be what type of function?

Hint:

Review problem 1-96.

Recall that $\Delta y$ represents the finite difference. What pattern do you see among the finite differences of the parabola $y = x^2$ ? What would the graph of those finite difference look like? Is this true for all parabolas?

Upward Parabola, vertex at the origin, with dashed slope triangles between the following points, with labeled for vertical legs: (negative 3, comma 9), & (negative 2, comma 4), label negative 5, (negative 2, comma 4), & (negative 1, comma 1), label negative 3, (negative 1, comma 1), & origin, label negative 1, (1, comma 1), & (2, comma 4), label 3, (2, comma 4), & (3, comma 9), label 5.

$\boldsymbol x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
$\boldsymbol{f(x)}$	$9$	$4$	$1$	$0$	$1$	$4$	$9$
$\boldsymbol{\Delta{y}}$	$\underset{\LARGE{\smile}}{-5}$ The difference between 9 and 4 is minus 5 $\underset{\LARGE{\smile}}{-3}$ The difference between 4 and 1 is minus 3 $\underset{\LARGE{\smile}}{-1}$ The difference between 1 and 0 is minus 1. $\underset{\LARGE{\smile}}{+1}$ The difference between 0 and 1 is positive 1. $\underset{\LARGE{\smile}}{+3}$ The difference between 1 and 4 is positive 3. $\underset{\LARGE{\smile}}{+5}$ The difference between 4 and 9 is positive 5.