### Home > A2C > Chapter 4 > Lesson 4.1.2 > Problem4-27

4-27.

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.

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.

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

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?

What does the value for $a$ represent?

Use the eTool below to graph the equations.
Click the link at right for the full version of the eTool: 4-27 HW eTool