Find the equation used to graph this parabola

https://www.desmos.com/calculator/dhqcqwzq9f

Surprised by Parabolas

KU Center for STEM Learning

Steven Obenhaus

steveobenhaus@ku.edu

Slide 2 of 91

Instructional Emphasis The course is designed to include and promote methods of discovery, problem solving, collaboration, and presentation of results. Ultimately, Functions and Modeling is intended to make students think critically; thus, it should not be delivered in a purely lecture format. Students should consistently work in groups of three or four to collaborate in developing results. Groups should be shuffled a few times over the semester to foster new collaborations and fresh ideas. Each exploration of the course presents an opportunity for the instructor to emphasize and connect mathematics content and concepts. The instructor should make it clear to students that they should be open to viewing some of the mathematics they have previously experienced with a new perspective and an open mind.Although this is not primarily an education course, the instructor should strive to emphasize content connections within the mathematics of secondary curriculum. The instructor should also model the dissemination of mathematics content through the use of Socratic questioning, facilitation of student explorations, and inquiry-based activities.

Deep Knowledge

Concept map

Where in the Functions course already?

“Proper use of the language of mathematics is emphasized.”

goo.gl/7zW3gR

𝑦=𝑎𝑥2+𝑏𝑥+𝑐What happens if …

• Hold a and b constant and vary c,

• Hold b and c constant and vary a,

• Hold a and c constant and vary b,

Shooting Einstein

(How many points determine a unique parabola?)

Connected to exploration 14.2- matrices

Determine equation of parabola through given points: (4,0),(3,5),(-1,1)

https://www.desmos.com/calculator/17fhgfm1wr

A.

B.

C.

1. What type of graph does each function generate?

2. What is the domain and range of “B”?

3. For “B”, what interval for t will generate a complete graph without any retracing?

Catching a Bus

(When is a problem finished?)