  ### Home > A2C > Chapter 7 > Lesson 7.3.1 > Problem7-158

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.

1. $y = 2x^{2} − 14x + 13$

13 is not the correct number for a complete square.
Move it to the opposite side of the equation.

$y − 13 = 2x^{2} − 14$

Factor out the 2 because it will not make a ncomplete square.n

$y − 13 = 2\left(x^{2} − 7x\right)$

$\left(x − ?\right)\left(x − ?\right) = x^{2} − 7x + ?^{2}$

What number does the ? above need to be?

It needs to be 3.5 (or seven-twelfths).

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.

Factor.

To find the domain and range, think about what the graph looks like.

1. $x = 2y^{2} − 6y − 11$

See the steps in part (a).

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?