Do Now Write a quadratic function in standard form that represents each area as a function of the width. A builder is designing a rectangular parking lot. She has 300 feet of fencing to enclose the parking lot around three sides.

12.2A: 1st and 2nd Differences SWBAT analyze tables of different functions using the 1st and 2nd differences to identify the function type.

Table A is linear because it is decreasing by the same amount. Which table do you think represents each type of function? Explain your reasoning. Table A is linear because it is decreasing by the same amount. Table B represents is quadratic because it decreases by less and less.

1st differences are the differences between successive output values when successive input values have a difference of 1. Calculate the 1st differences for each function. What patterns do you notice? 1st Difference Table A 1st Difference Table B 2nd differences are the differences between consecutive values of the 1st differences. Calculate the 2nd differences for each function. What patterns do you notice? 2nd Difference Table A 2nd Difference Table B

Reflection: How do the signs of the 1st differences for a linear function relate to the graph either increasing or decreasing? If the signs of the 1st differences are positive, the linear function is increasing. If the signs of the 1st differences are negative, the linear function is decreasing.

2. How do the signs of the 1st differences and the signs of the 2nd differences for quadratic functions relate to the graph of the quadratic either increasing or decreasing or opening upward or downward? When the 1st differences are negative, the quadratic is decreasing. When the 1st differences are positive, the quadratic is increasing. If the 2nd differences are positive, the parabola opens upward. If the second differences are negative, then the parabola opens downward.