options: Understand the relationship between zeros and factors of polynomials.

Use properties of operations to generate equivalent expressions.

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

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

Add and subtract within 20.

Use the four operations with whole numbers to solve problems.

Solve equations and inequalities in one variable.

Write expressions in equivalent forms to solve problems.

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

Multiply and divide within 100.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use polynomial identities to solve problems.

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

Work with radicals and integer exponents.

Work with addition and subtraction equations.

Represent and solve problems involving multiplication and division.

Create equations that describe numbers or relationships

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

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

Write and interpret numerical expressions.

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

Represent and solve equations and inequalities graphically.

Perform arithmetic operations on polynomials.

Reason about and solve one-variable equations and inequalities.

Represent and analyze quantitative relationships between dependent and independent variables.

Solve systems of equations.

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

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

Interpret the structure of expressions.

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

Generate and analyze patterns.

Rewrite rational expressions.

Gain familiarity with factors and multiples.
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: 0