options: Interpret the structure of expressions.

Rewrite rational expressions.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Work with equal groups of objects to gain foundations for multiplication.

Write expressions in equivalent forms to solve problems.

Work with radicals and integer exponents.

Analyze patterns and relationships.

Represent and analyze quantitative relationships between dependent and independent variables.

Use polynomial identities to solve problems.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand the connections between proportional relationships, lines, and linear equations.

Represent and solve problems involving addition and subtraction.

Create equations that describe numbers or relationships

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Use properties of operations to generate equivalent expressions.

Solve systems of equations.

Solve equations and inequalities in one variable.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.

Represent and solve equations and inequalities graphically.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Gain familiarity with factors and multiples.

Understand solving equations as a process of reasoning and explain the reasoning.

Generate and analyze patterns.

Write and interpret numerical expressions.

Use the four operations with whole numbers to solve problems.

Understand properties of multiplication and the relationship between multiplication and division.

Understand and apply properties of operations and the relationship between addition and subtraction.

Multiply and divide within 100.

Understand the relationship between zeros and factors of polynomials.

Add and subtract within 20.

Perform arithmetic operations on polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with addition and subtraction equations.
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.
$${g(x)={2\over3} \left({x-{1\over9}} \right)^2 -{8\over27}}$$


correct_option_index: 16

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