## Reflection: Developing a Conceptual Understanding What if We Start With the Axis of Symmetry? - Section 2: Review the formulas: Axis of Symmetry and Discriminant

This unit on quadratic functions is fascinating to teach.  On the one hand, the "new" material of factoring, graphing parabolas, and learning about the features of quadratic functions is often enough to engage all kids in some rich explorations.  On the other hand, this unit is really where the rubber meets the road: to achieve high levels of mastery, students must apply all sorts of knowledge about signed arithmetic, evaluating expressions and irrational numbers.  The more comfortable students are with algebraic manipulation and all the other algebraic ideas that preceded this unit, the better off they'll be here.

But at the same time, even students who have struggled throughout the year have some huge aha moments when they're exposed to the new, weirder world of non-linear functions like quadratics.

Take for instance, the axis of symmetry.  All students buy the idea that this is an effective tool for sketching parabolas.  They feel the thrill of understanding to see that each root is the same distance from the axis of symmetry.  But then, despite all of that conceptual meaning-making, I always have students who have trouble identifying coefficients, or who get hung up on figuring out where the negative sign goes in the formula for the axis of symmetry: is it in front of the whole fraction, or is it on the 'b'?  It's one thing for everyone to determine the axis of symmetry for y = x^2 + 10x + 21.  It's a big challenge for some kids to do the same for y = 21 - 7x - 3x^2, for reasons that have little to do with their understanding of quadratic functions.

Which makes this unit such fertile ground for differentiation.  I can get broad concepts across to everyone, and then when we get to practicing, there are many opportunities to re-teach/reinforce/remediate foundational skills -- or to raise the bar even higher.

Developing a Conceptual Understanding: Where does that negative sign go?

# What if We Start With the Axis of Symmetry?

Unit 10: Quadratic Functions
Lesson 13 of 21

## Big Idea: An investigation of the relationship between the discriminant and the axis of symmetry lays foundations for students to understand the quadratic formula.

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Subject(s):
Math, quadratic formula, quadratic functions, Quadratic Equations, graphing functions, axis of symmetry, Growth Mindset, Algebra 1
53 minutes

### James Dunseith

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