Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
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Exercise 1 Page 66

The graph of has been scaled horizontally. Use a point on the graph of to determine the horizontal scale.

To obtain we must translate the graph of units up and then stretch it horizontally by a factor of

Practice makes perfect

We are given the graphs of two functions, namely, and

First, we see that the vertex of is units above the vertex of We will start by translating the graph of up units.
Now, let's plot and on the same coordinate plane and compare them.

We see that the graphs of and still do not match. However, we can see that the graph of is wider, which means that we have to make a horizontal stretch. In other words,

To figure out the scale factor, we will use the fact that
Next, we substitute and solve the equation for
Solve for
Since must be positive, we will discard the negative option. Now, we are ready to write our function in terms of
In conclusion, to obtain we must translate the graph of units up and then stretch it horizontally by a factor of