### Home > CCA2 > Chapter 2 > Lesson 2.1.2 > Problem2-24

2-24.

Consider the equations $y=3(x−1)^2−5$ and $y=3x^2−6x−2$. 2-24 HW eTool (Desmos). Homework Help ✎.

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: CCA2 2-24 HW eTool