In this lesson, students evaluate functions at different values to compare them and rewrite quadratic functions into vertex form to find the vertex. In the associated Algebra 1 lesson, students use the vertex form of quadratic functions to find the vertex and solve problems using the maximum and minimum. The work of this lesson supports students by improving their fluency with evaluating functions and changing the form of an equation into a more useful one. Students look for and make use of structure (MP7) when they use an equation in standard or factored form to identify the vertex of a graph.
Lesson overview
- 23.1 Warm-up: Math Talk: Evaluating Functions (5 minutes)
- 23.2 Activity: Comparing Functions (15 minutes)
- 23.3 Activity: Finding the Vertex (20 minutes)
Learning goals:
- Determine which \(x\)-value has a greater \(y\)-coordinate for a given function.
- Write quadratic equations in vertex form and find the vertex.
Learning goals (student facing):
- Let’s evaluate and compare functions.
Standards:
- This lesson builds towards the standard: CCSS.HSF-IF.CMO.A1.IF.C
IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.