options: Use polynomial identities to solve problems.

Solve equations and inequalities in one variable.

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

Use properties of operations to generate equivalent expressions.

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

Interpret the structure of expressions.

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.

Analyze patterns and relationships.

Reason about and solve one-variable equations and inequalities.

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

Work with addition and subtraction equations.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Write and interpret numerical expressions.

Perform arithmetic operations on polynomials.

Represent and solve equations and inequalities graphically.

Understand the relationship between zeros and factors of polynomials.

Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Multiply and divide within 100.

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

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

Write expressions in equivalent forms to solve problems.

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

Solve systems of equations.

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

Add and subtract within 20.

Represent and solve problems involving multiplication and division.

Use the four operations with whole numbers to solve problems.

Work with radicals and integer exponents.

Rewrite rational expressions.

Generate and analyze patterns.

Create equations that describe numbers or relationships
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: 17