options: Use properties of operations to generate equivalent expressions.

Represent and solve equations and inequalities graphically.

Generate and analyze patterns.

Add and subtract within 20.

Understand the relationship between zeros and factors of polynomials.

Reason about and solve one-variable equations and inequalities.

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

Represent and solve problems involving addition and subtraction.

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

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

Rewrite rational expressions.

Write expressions in equivalent forms to solve problems.

Work with radicals and integer exponents.

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

Represent and solve problems involving multiplication and division.

Work with addition and subtraction equations.

Analyze patterns and relationships.

Represent and analyze quantitative relationships between dependent and independent variables.

Use polynomial identities to solve problems.

Perform arithmetic operations on polynomials.

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

Gain familiarity with factors and multiples.

Solve systems of equations.

Solve equations and inequalities in one variable.

Write and interpret numerical expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Create equations that describe numbers or relationships

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

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

Multiply and divide within 100.

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

Use the four operations with whole numbers to solve problems.

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

Interpret the structure of expressions.
problem_activity: Problem 1
A business is marketing its product and has collected data on sales and prices for the past few years. The company, through careful modeling, has determined that their profit is dependent upon the selling price of the item and that it follows a quadratic model.
The function below describes the profit,
$$P$$
, dependent upon the selling price,
$$s$$
, of its product.
$$P(s)=-20s^2+1,400s-12,000$$
a.  Write the function in intercept form and identify the roots.
b.  Explain what the roots mean in context of the situation.
c.  Write the function in vertex form and identify the vertex.
d.  Explain what the vertex means in context of the situation.
Problem 2
The height,
$$h$$
, in feet, of a projectile launched upward from a bridge is given by
$$ h=-16t^2+16t+96$$
, where
$$t$$
is time in seconds.
Write the equation in vertex form.
How long does it take for the projectile to reach maximum height?
What is the maximum height of the projectile?


correct_option_index: 11