Algebra II Lesson

Three Forms of a Quadratic: Vertex, Factored, and Standard

Shared by A STEM Educator

11th grade HonorsBTC Style / Thinking Classrooms90 min

Learning Objective

Students will fluently convert quadratic functions among standard, vertex, and factored forms and use each form strategically to identify the vertex, axis of symmetry, and x- and y-intercepts.

Lesson Overview

Students progress from identifying key features directly from vertex and factored forms, through converting between all three forms, culminating in choosing the optimal form to extract any feature efficiently.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors)
Pencils and notebook paper

Scaffolded Task Progression

1Task 1

The function

f (x) = (x - 3)^{2} + 4

is written in vertex form.
a) State the vertex.b) State the axis of symmetry.c) Does the parabola open up or down? [ Interactive graph / diagram, available in the full lesson ]

2Task 2

The function

g (x) = (x + 2)^{2} - 5

is written in vertex form.
a) State the vertex.b) State the axis of symmetry.c) Does the parabola open up or down? [ Interactive graph / diagram, available in the full lesson ]

3Task 3

The function

h (x) = - 2 (x - 1)^{2} + 9

is written in vertex form.
a) State the vertex and axis of symmetry.b) Does it open up or down? Is it wider or narrower than

y = x^{2}

?c) What is the maximum value of the function? [ Interactive graph / diagram, available in the full lesson ]

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