Converting Between Quadratic Forms Worksheet

Six quadratic functions are each given in one of three forms — standard, vertex, or intercept — and students derive the remaining two forms and sketch the graph.

An educational teaching resource from Eight Gone Sideways entitled Quadratic Equations – Converting Forms Worksheet downloadable at Teach Simple.

Year groups: Years 10–13
File type: PDF
Preparation: Print ready

Updated Sep 16, 2022

Subject: Algebra, Maths
Topic: Standard Form, Algebra
Resource types: Worksheets, Worksheets & Printables
Preparation: Print ready

From the author

About this resource

This is a Quadratic Equations Worksheet that will give students practice with converting forms.

There are 6 problems - 3 per page.

Students will explore standard form, vertex form, intercept form and graphing.

In the classroom

Teaching tips & learning objectives

Learning objectives

Convert a quadratic function from standard form to vertex form.
Convert a quadratic function from standard form to intercept (factored) form.
Convert a quadratic function from vertex form to standard form and to intercept form.
Convert a quadratic function from intercept form to standard form and to vertex form.
Graph a quadratic function represented in any of the three forms.

Teaching tips

Point out which form is already given in each row before students start, since the required conversion path changes function to function.
Review completing the square before assigning rows that start in standard form, since that is the typical route to vertex form.
Use the completed answer chart to spot-check factoring or expansion errors before students move to the graphing column.

Skills covered

Standard-to-vertex conversion — students complete the square to rewrite standard-form functions such as f(x) = 2x² + 4x − 6 in vertex form.
Standard-to-intercept conversion — students factor standard-form functions to find their intercept (factored) form.
Vertex/intercept-to-standard expansion — students expand vertex- or intercept-form expressions back into standard form.
Graphing from multiple representations — students sketch each function's graph after determining all three algebraic forms.

Good to know

Questions teachers ask about this resource

Does every function start from the same form?

No — the given form rotates row by row: some functions start in standard form, others in vertex form or intercept form, so students practice conversions in every direction rather than one repeated pattern.

Are negative or fractional leading coefficients included?

Yes — several functions use negative or fractional coefficients, for example f(x) = -2/3x² - 4/3x + 16/3, so the practice goes beyond simple integer quadratics.

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Resource details

Concepts & topics

Core concepts

Standard form
Vertex form
Intercept form
Quadratic functions
Completing the square

Topics

Standard Form Algebra Mixed Functions Converting Forms Quadratic Equations Quadratic Worksheets Quadratic Equations Worksheets Quadratic Function and Equations Worksheet Quadratic Equations Practice Worksheets

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Categories this resource belongs to

Algebra Maths Worksheets Worksheets & Printables Year 13 Year 12

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