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4-27.

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