Consider the equations $y=3(x−1)^2−5$ and $y=3x^2−6x−2$.

1. Verify that they are equivalent by creating a table or graph for each equation.

   Hint (a):

   Here are a couple of points on the table. Make sure you get these points and continue both of your tables for at least the $x$-values given.

   $x$	$y$
   $-2$	$22$
   $-1$
   $0$
   $1$	$-5$
   $2$

2. Show algebraically that these two equations are equivalent by starting with one form and showing how to get the other.

   Answer (b):

   $y=3(x−1)^2−5\\ y=3(x^2−2x+1)−5\\y=3x^2−6x+3−5\\y=3x^2−6x−2$

3. Notice that the value for $a$ is $3$ in both forms of the equation, but that the numbers for $b$ and $c$ are different from the numbers for $h$ and $k$. Why do you think the value for $a$ would be the same number in both forms of the equation?

   Hint (c):

   What does the value for $a$ represent?