Alg1.6 Introduction to Quadratic Functions
- I can create drawings, tables, and graphs that represent the area of a garden.
- I can recognize a situation represented by a graph that increases then decreases.
- I can describe how a pattern is growing.
- I can tell whether a pattern is growing linearly, exponentially, or quadratically.
- I know a quadratic expression has a squared term.
- 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.
- I can explain using graphs, tables, or calculations that exponential functions eventually grow faster than quadratic functions.
- I can explain the meaning of the terms in a quadratic expression that represents the height of a falling object.
- I can use tables, graphs and equations to represent the height of a falling object.
- I can create quadratic functions and graphs that represent a situation.
- I can relate the vertex of a graph and the zeros of a function to a situation.
- I know that the domain of a function can depend on the situation it represents.
- I can choose a domain that makes sense in a revenue situation.
- I can model revenue with quadratic functions and graphs.
- I can relate the vertex of a graph and the zeros of a function to a revenue situation.
- I can rewrite quadratic expressions in different forms by using an area diagram or the distributive property.
- I can rewrite quadratic expressions given in factored form in standard form using either the distributive property or a diagram.
- I know the difference between “factored form” and “standard form.”
- I can explain the meaning of the intercepts on a graph of a quadratic function in terms of the situation it represents.
- I know how the numbers in the factored form of a quadratic expression relate to the intercepts of its graph.
- I can graph a quadratic function given in factored form.
- I know how to find the vertex and $y$-intercept of the graph of a quadratic function in factored form without graphing it first.
- I can explain how the $a$ and $c$ in $y=ax^2+bx+c$ affect the graph of the equation.
- I understand how graphs, tables, and equations that represent the same quadratic function are related.
- I can explain how the $b$ in $y=ax^2+bx+c$ affects the graph of the equation.
- I can match equations given in standard and factored form with their graph.
- I can explain how a quadratic equation and its graph relate to a situation.
- I can recognize the “vertex form” of a quadratic equation.
- I can relate the numbers in the vertex form of a quadratic equation to its graph.
- I can graph a quadratic function given in vertex form, showing a maximum or minimum and the $y$-intercept.
- I know how to find a maximum or a minimum of a quadratic function given in vertex form without first graphing it.
- I can describe how changing a number in the vertex form of a quadratic function affects its graph.