SL AI – Quadratic Graphs

Completing the Square 1 (where a is 1)

Practice your own completing the square and use the Applet below to check your answers.

Completing the Square 2 (where a is not 1)

Practice your own completing the square and use the Applet below to check your answers.

Graphing in Completed the Square Form

Move the sliders around on the Applet below.

What is the connection between the vertex and the equation of the graph?

The Quadratic Graph
The quadratic graph, using a Casio GDC

Completing the Square Form

Questions and Answers












Teacher Resources

SSDD Completing the Square

Same surface different deep problems. 4 Variants.

Desmos Properties of Quadratic Functions

Quadratic functions, and an introduction to the determinant. By Bob Lochel.

Desmos Talkers & Drawers - Quadratic

Students will generate a need to use less informal language and more formal language when describing quadratic relations. One student will attempt to “describe” (without using their hands) a graph for their partner to sketch (who can’t talk). Then the two will swap roles. By Jonorr.

Desmos Polygraph Parabolas

We have designed Polygraph to foster the pleasure and the power of words without the drudgery of the lists. With Polygraph, Desmos provides tools for developing informal language into formal vocabulary. Because words should result from a need to describe our world—this is where they gain their power.

Desmos Understanding (h,k)

This Custom Polygraph is designed to spark vocabulary-rich conversations about the impact of (h, k) on the vertex form equation of a parabola. Key vocabulary that may appear in student questions includes: translation, shift, slide, horizontal, vertical, vertex, line of symmetry, axis, quadrant, x-value, and y-value.

Desmos Polygraph: Parabolas, Part 2

This activity follows up on Polygraph: Parabolas, using the discussions (and students’ informal language) in that activity to develop academic vocabulary related to the graphs of quadratic functions. For this activity, we recommend that students using a screen reader pair up with a sighted partner.

Desmos Match My Parabola

In this activity, students work through a series of scaffolded quadratic graphing challenges to develop their proficiency with standard, vertex, factored, and other quadratic function forms.

Desmos Parabola Card Sort

The first screen is a sketch. I give the students a parabola in standard form to sketch and follow their work on my tablet dashboard. We sketched 3 or 4 parabolas and I had an idea where I needed to intervene during card sort. Match a parabola to standard form card sort. By Paul Jorgens.

Desmos Quadratic pictures

Students match a quadratic in either standard, vertex or factored form to a picture. They then need to choose an appropriate form for matching and finally, they choose a picture themselves and fit a quadratic curve. By Becky Hall.

Desmos Parabola Slalom

In this activity, students work through a series of slalom-themed challenges to strengthen (and stretch) their algebraic and graphical understanding of parabolas. Activity inspired by Paul Jorgens.

Desmos Two Truths and a Lie: Parabolas

Students will practice their understanding of the features and vocabulary of a parabola by creating a parabola, writing two true and one false statement about it, and inviting their peers to separate truth from lies.

Desmos Polygraph Totes

Students can discuss asymptotes and other characteristics. By Andrew Stadel.