CPM Homework Help : A2C Problem 7-158

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Home > A2C > Chapter Ch7 > Lesson 7.3.1 > Problem 7-158

7-158.

Complete the square to change each equation below to graphing form. Find the domain and range of each relation and determine if it is a function.

$y = 2x^{2} − 14x + 13$
Step 1(a):
13 is not the correct number for a complete square.
Move it to the opposite side of the equation.
$y − 13 = 2x^{2} − 14$
Step 2(a):
Factor out the 2 because it will not make a ⁿcomplete square.ⁿ
$y − 13 = 2\left(x^{2} − 7x\right)$
Step 3(a):
$\left(x − ?\right)\left(x − ?\right) = x^{2} − 7x + ?^{2}$
What number does the ? above need to be?
It needs to be 3.5 (or seven-twelfths).
Step 4(a)
3.5² needs to be added in the parenthesis.
This is actually 2(3.5²) being added on the right side.
Add 2(3.5²) to the left side as well.
Step 5(a):
Factor.
Hint (a):
To find the domain and range, think about what the graph looks like.

$x = 2y^{2} − 6y − 11$
Hint (b):
See the steps in part (a).
More Help (b):
The graph in part (a) was a $y = x^{2}$ parabola.
This in an $x = y^{2}$ parabola.
How does this change the graph and hence the domain and range?

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