  ### Home > INT3 > Chapter 2 > Lesson 2.2.5 > Problem2-125

2-125.

Consider the functions $y=3(x-1)^2-5$ and $y=3x^2-6x-2$. 2-125 HW eTool (Desmos). Homework Help ✎

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

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 functions 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 function, but that the values for $b$ and $c$ are different from the values for $h$ and $k$. Why is the value for $a$ the same in both forms of the function?

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: Int3 2-125 HW eTool