options: Write expressions in equivalent forms to solve problems.

Understand the relationship between zeros and factors of polynomials.

Represent and solve equations and inequalities graphically.

Reason about and solve one-variable equations and inequalities.

Analyze patterns and relationships.

Use the four operations with whole numbers to solve problems.

Use properties of operations to generate equivalent expressions.

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

Write and interpret numerical expressions.

Create equations that describe numbers or relationships

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

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

Rewrite rational expressions.

Perform arithmetic operations on polynomials.

Represent and solve problems involving addition and subtraction.

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

Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

Interpret the structure of expressions.

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

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

Use polynomial identities to solve problems.

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

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

Represent and analyze quantitative relationships between dependent and independent variables.

Solve equations and inequalities in one variable.

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

Solve systems of equations.

Add and subtract within 20.

Generate and analyze patterns.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with addition and subtraction equations.

Multiply and divide within 100.

Represent and solve problems involving multiplication and division.
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: 1