options: Reason about and solve one-variable equations and inequalities.

Create equations that describe numbers or relationships

Multiply and divide within 100.

Perform arithmetic operations on polynomials.

Solve equations and inequalities in one variable.

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

Add and subtract within 20.

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

Work with radicals and integer exponents.

Represent and solve problems involving multiplication and division.

Use polynomial identities to solve problems.

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

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

Represent and analyze quantitative relationships between dependent and independent variables.

Analyze patterns and relationships.

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

Represent and solve equations and inequalities graphically.

Interpret the structure of expressions.

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

Represent and solve problems involving addition and subtraction.

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

Write expressions in equivalent forms to solve problems.

Work with addition and subtraction equations.

Solve systems of equations.

Use properties of operations to generate equivalent expressions.

Write and interpret numerical expressions.

Generate and analyze patterns.

Use the four operations with whole numbers to solve problems.

Rewrite rational expressions.

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

Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand the relationship between zeros and factors of polynomials.

Understand the connections between proportional relationships, lines, and linear equations.
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: 32