options: Represent and solve equations and inequalities graphically.

Solve systems of equations.

Represent and solve problems involving addition and subtraction.

Write and interpret numerical expressions.

Represent and solve problems involving multiplication and division.

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

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

Solve equations and inequalities in one variable.

Work with radicals and integer exponents.

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

Rewrite rational expressions.

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

Generate and analyze patterns.

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

Create equations that describe numbers or relationships

Interpret the structure of expressions.

Reason about and solve one-variable equations and inequalities.

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

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

Understand the relationship between zeros and factors of polynomials.

Add and subtract within 20.

Write expressions in equivalent forms to solve problems.

Gain familiarity with factors and multiples.

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

Use properties of operations to generate equivalent expressions.

Perform arithmetic operations on polynomials.

Work with addition and subtraction equations.

Analyze patterns and relationships.

Represent and analyze quantitative relationships between dependent and independent variables.

Use the four operations with whole numbers to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Use polynomial identities to solve problems.

Multiply and divide within 100.
problem_activity: Task
Suppose $f$ is a quadratic function given by the equation $f(x) = ax^2 + bx + c$
where $a,b,c$ are real numbers and $a$ is non-zero.
Explain why $f$ can have at most two roots; that is explain why there can be at most two distinct real numbers $r_1,r_2$ so that $f(r_1) = f(r_2) = 0$.
Give examples to show that it is possible for $f$ to have zero, one, or two
real roots.


correct_option_index: 19