Is Goblins free for teachers?

Yes. Goblins offers a generous free tier that includes 1 live feedback assignment per week, insights on student mastery and replays, and the ability to upload your own content. The Max plan adds unlimited assignments, superadaptive mode, grade exports, standards growth reports, and SSO/LMS integration, with per-student pricing for schools and districts.

How does Goblins work?

Three simple steps: (1) Share an assignment from thousands of standards-aligned topics using a share code. (2) Students speak and draw their thinking naturally, and Goblins responds with Socratic questioning that sounds just like their teacher. (3) Teachers get real-time formative insights showing what students struggle with and suggestions to inform instruction.

Does Goblins prevent cheating?

Yes. Goblins uses a purpose-trained AI model that evaluates cheating signals in real time. It can detect when students are copying answers, using external tools inappropriately, or not genuinely working through problems. Copy-pasting answers is also blocked.

Can I use my own voice with Goblins?

Yes. Teachers can record their voice and take a selfie to create a custom 3D avatar in about 30 seconds. Students then hear help in their own teacher's voice and see a familiar face, making the experience more personal and effective.

What math levels does Goblins cover?

Goblins covers math from Grade 5 through AP Calculus, including thousands of standards-aligned topics. Teachers can also upload their own content for custom assignments at any level.

Is Goblins FERPA compliant?

Yes. Goblins is FERPA and state compliant. Student data privacy and security are a top priority.

Does Goblins support English Language Learners?

Yes. Goblins supports 30+ languages so teachers don't have to translate every worksheet. It is especially helpful for ELL students who need accessible math instruction in their native language.

M.A1HS.43.b

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Example Problems

What is the minimum of the following function?

f(x) = 4(x - 5)^2 + 2

What is the minimum of the following function?

f(x) = 6(x - 4)^2 + 1

What is the minimum of the following function?

f(x) = 3(x - 1)^2 + 7

Khan Academy Resources

Solving quadratics by completing the square Graphing quadratics review Completing the square review Completing the square (intermediate)Completing the square Graph parabolas in all forms Graph quadratics in standard form Quadratic word problems (standard form)Interpret quadratic models Completing the square (intro)Features of quadratic functions Features of quadratic functions: strategy Worked example: completing the square (leading coefficient ≠ 1)Completing the square Vertex & axis of symmetry of a parabola Worked example: Completing the square (intro)Solving quadratics by completing the square: no solution Finding the vertex of a parabola in standard form Comparing maximum points of quadratic functions Worked examples: Forms & features of quadratic functions Interpret quadratic models: Vertex form Graphing quadratics: standard form Worked example: Rewriting & solving equations by completing the square Worked example: Rewriting expressions by completing the square

1-on-1 AI tutoring aligned to M.A1HS.43.b. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

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