standard_description: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
problem_activity: Problem 1
Which of the following quadratic functions will result in non-real solutions?
$${{1\over2}(x-1)^2-5=0}$$
$${{1\over2}(x-1)^2+5=0}$$
$$-{{1\over2}(x-1)^2+5=0}$$
$$-{{1\over2}(x-1)^2-5=0}$$
Explain your resoning.
Problem 2
Solve the following quadratic function. Identify the number and kind of solutions.
$${g(x)={2\over3} \left({x-{1\over9}} \right)^2 -{8\over27}}$$


aligns: no