ALEX Classroom Resource

  

Concavity and Inflection Solved Video

  Classroom Resource Information  

Title:

 Concavity and Inflection Solved Video

URL:

 https://www.ck12.org/c/calculus/concavity-and-inflection/lecture/Concavity-and-Inflection-Solved/?referrer=concept_details

Content Source:

 Other
CK-12
Type: Audio/Video

Overview:

This video will explain how to solve functions to determine if the relationship between the variables shows concavity or inflection.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Mathematical Modeling
15. Use regression with statistical graphing technology to determine an equation that best fits a set of bivariate data, including nonlinear patterns.

Examples: global temperatures, stock market values, hours of daylight, animal population, carbon dating measurements, online streaming viewership

a. Create a scatter plot with a sufficient number of data points to predict a pattern.

b. Describe the overall relationship between two quantitative variables (increase, decrease, linearity, concavity, extrema, inflection) or pattern of change.

c. Make a prediction based upon patterns.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Can use graphing technology to plot a scatter diagram.
  • Can describe a relationship if one exists between points.
  • Can find a regression equation using graphing technology.
  • Can use the regression equation to make a prediction.
Teacher Vocabulary:
  • Regression Equation
  • "Best Fit"
  • Bivariate Data
  • Linear Pattern
  • Non-linear pattern
  • Scatter Plot
  • Quantitative Variable
  • Extrema
  • Inflection
Knowledge:
Students know:
  • how to plot points using graphing technology.
  • how to find a regression equation using graphing technology.
  • how to use a regression equation to make a prediction.
Skills:
Students are able to:
  • plot points.
  • Distinguish between linear and nonlinear functions.
  • Use graphing technology.
Understanding:
Students understand that:
  • Regression equations can be used to model data.
  • Graphing technology helps us find regression equations.
  • The regression equation can be used to make a prediction.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
MMOD.15.1: Define bivariate scatter plot, outlier, cluster, linear, nonlinear, positive and negative association, slope, intercept, linear, equation, concave up, concave down, and bivariate.
MMOD.15.2: Make a prediction based upon patterns.
MMOD.15.3: Describe patterns found in a scatter plot.
MMOD.15.4: Demonstrate how to label and plot information on a scatter plot (dot plot).
MMOD.15.5: Distinguish the difference between positive and negative correlation.
MMOD.15.6: When given data points, use technology to find the equation of a line.

Prior Knowledge Skills:
  • Define bivariate scatter plot, quantitative data, outlier, cluster, linear, nonlinear, and positive and negative association.
  • Describe patterns found in a scatter plot.
  • Demonstrate how to label and plot information on a scatter plot (dot plot).
  • Distinguish the difference between positive and negative correlation.
  • Recall how to describe the spread of the scatter plot (dot plot).
  • Create a scatter plot and line of best fit using data from a spreadsheet.
  • Organize and display bivariate quatitative data using a scatter plot, and extend from simple cases by hand to more complex cases involving a large data set using technology.
  • Create a scatter plot of data.
  • Calculate the fit of the function to the data by examining residuals.
Tags: concavity, decreasing, derivative, function, graph, increasing, inflection, mathematical modeling, point, test
License Type: Custom Permission Type
See Terms: https://www.ck12info.org/terms-of-use/
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityVideo resources: includes closed captioning or subtitles
Comments
  This resource provided by:  
Author: Hannah Bradley
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