## Reflection: Developing a Conceptual Understanding Features of a Parabola - Section 2: Complete Your Gallery Walk, With One New Instruction

As we continue to shift our emphasis from the algebraic manipulation of quadratic expressions to a study of the graphs of quadratic functions, I still haven't named "f(x) = (x - h)^2 + k" as "vertex form".   In fact, I haven't even hurried to replace the "+" sign that was on "Quadratic Functions in Three Forms" to the "-" sign that is traditionally used in the vertex form of a quadratic function.

But we're getting there.

When students started their work on Quadratic Functions in Three forms at the beginning of the week, I made sure to name the first two columns of that assignment as "standard form" and "factored form".  For the last column, however, I told students that we'd figure out what to call this eventually, and that I was open to suggestions.  In the next lesson, students recognized that this form was easiest to manipulate on an interactive graph.  In last few days, as we've gotten rolling on the gallery walk, students have learned to recognize and label the vertex of a parabola.

As they finish their gallery walks, I'll often assign the additional extension of writing each function in vertex form, even though we still don't have those words yet.  Once students rewrite their functions that way, and they look at the coordinates of each vertex on the graph, they are thrilled to discover this connection for themselves, and instead of being told, "hey, this is called vertex form," they find those words on their own - and that feels as natural as can be!

What should we call f(x) = (x + h)^2 + k?
Developing a Conceptual Understanding: What should we call f(x) = (x + h)^2 + k?

# Features of a Parabola

Lesson 9 of 21

## Big Idea: Students finish up the Quadratic Functions Gallery Walk and begin to spot connections between where the roots and where the vertex are located.

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Subject(s):
Math, quadratic functions, Quadratic Equations, graphing functions, Gallery Walk, Growth Mindset, Algebra 1
35 minutes

### James Dunseith

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