Geometry, a novel twist on Match My Graph, and two Calculus activities are what we have in store for you in this week’s Friday Five. But first, we begin with a simple solution to a challenging problem—putting a quadratic function into vertex form.

## Where Is the Vertex?

Let’s say you have a quadratic function in standard form, and you want to write it in vertex form. What do you do? Must you complete the square or factor it first? Must you remember a formula?

Why, no! You can use the y-intercept!

A recent letter to editor at Mathematics Teacher laid out the idea and Desmos’s own Christopher Danielson adapted it for Activity Builder. Now go run this activity—for yourself, for your Algebra 2 students, or your preservice math teachers.

## Target Practice

From Jon Orr, we have this lovely twist on Match My Graph. Send one or more functions through the indicated points. Now try to do it with fewer functions. And don’t get too smug on those first few screens.

## Lines, Transversals, and Angles

Geometry and a clever use of movable points—these are the things the mind of Michael Fenton brings your way this week. This activity provides a quick introduction (or review) of relationships between angles in parallel (and non-paralle!) lines cut by a transversal.

## What Is the Derivative, Anyway?

Leigh Nataro increases the collection of Calculus activities with this contribution that connects a function’s derivative to the intervals where the function increases and decreases. When your calculus students are on their way to learning about the role of the first derivative in finding a function’s extrema, this is your activity.

## Daylight Hours

Joshua Bowman demonstrates some serious calculator skills in assembling this astronomy/calculus mashup. How does the number of hours of daylight vary through the year at your latitude? What about at that of your grandmother? Or of Santa Claus? Have a go at Joshua’s activity to find out, and to think about the relevance of derivatives to all of this.