standard_description: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
problem_activity: Problem 1
Below is the parent function of a quadratic function:
[IMG]
Given the equation in vertex form and the corresponding graph, identify the transformations to each function.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width:80%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Equation"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Graph"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Transformation(s)"}]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${g(x)=(x+1)^2+3}$$"}]}, {"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1b.png", "style": "height:200px; width:200px"}}]}, {}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${r(x)=-2(x-1)^2}$$"}]}, {"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1c.png", "style": "height:200px; width:200px"}}]}, {}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${t(x)=(2x-1)^2}$$"}]}, {"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1d.png", "style": "height:200px; width:200px"}}]}, {}]}]}]}]}
Problem 2
A quadratic equation is
decreasing over the interval
$${-\infty < x < 3}$$
increasing over the interval
$${3 < x < \infty}$$
and has a rate of change of zero at
$${x=3}$$
.
Describe how each of the three graphs below fit this description.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width:90%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2a.png", "style": "height:282px; width:200px"}}]}, {"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2b.png", "style": "height:285px; width:200px"}}]}, {"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2c.png", "style": "height:287px; width:200px"}}]}]}]}]}]}


aligns: no