Building Quadratic Functions from Geometric Patterns

Building Quadratic Functions from Geometric Patterns

Let’s describe some other geometric patterns.

• I can recognize quadratic functions written in different ways.

• I can use information from a pattern of shapes to write a quadratic function.

• I know that, in a pattern of shapes, the step number is the input and the number of squares is the output.

​Learning Targets

quadratic function

A function where the output is given by a quadratic expression in the input.

Open Ended

Write an expression to represent the area of Figure B when the side lengths of the large square is 4 units , or x units, or 4x units, or x + 3 Units.

Open Ended

Write an expression to represent the area of Figure B, a large square with a smaller square removed, with side length of is 4 units , or x units, or 4x units, or x + 3 Units. for the large square.

Open Ended

Write an expression to represent the area of Figure C which is composed of two large squares with one smaller square added. with side lengths of 4 units , or x units, or 4x units, or x + 3 Units.. for the larger square.

Open Ended

If the pattern continues, How many small squares are inin Step 5 and Step 18?

Open Ended

Write an equation to represent the relationship between the step number n and the number of squares y. Be prepared to explain how each part of your equation relates to the pattern. (If you get stuck, try making a table.)

Open Ended

How many squares would be in the next step in the pattern.

Open Ended

Kiran says that the pattern is growing linearly because as the step number goes up by 1, the number of rows and the number of columns also increase by 1.

Agree or disagree? Explain

Open Ended

To represent the number of squares after n steps, Diego and Jada wrote different equations. Diego wrote the equation f(n) = n(n + 2). Jada wrote the equation f(n) = n² + 2n. Are either Diego or Jada correct? Explain your reasoning.

To determine if the relationship between two quantities represents a quadratic function:

• Determine if there is only one output for every input (function).

• Additionally one quantity is in some way squared or multiplied by itself to obtain the second quantity.

• See if the relationship can be expressed with a squared term

​Quadratic Relationship Features

• I can recognize quadratic functions written in different ways.

• I can use information from a pattern of shapes to write a quadratic function.

• I know that, in a pattern of shapes, the step number is the input and the number of squares is the output.

​Learning Targets

Open Ended

Write an equation to represent the relationship between the step number and the number of squares in the pattern. Briefly describe how each part of the equation relates to the pattern.