Quadratic Characteristics Worksheet

About this resource

What's inside this resource

Quadratic Characteristics - Intercept Form - Worksheet provides algebra students practice identifying key attributes of quadratic functions graphed in intercept form. This 2-page printable PDF comprises 8 total problems for learners to analyze quadratic equations presented graphically. By completing this scaffolding exercise individually, in small groups, or as a whole class activity, students reinforce intercept form concepts like determining the x- and y-axis intercepts, vertex, domain and range, and lines of symmetry. This standards-aligned quadratic functions worksheet is well-suited for grade 9-12 algebra, for use as in-class practice, group work, formative assessment, or homework to supplement instruction on analyzing and interpreting characteristics of quadratic functions in intercept form.

What's included

A student page of four graphed quadratics, each with nine blanks to complete, headed "Complete the following characteristics for each function that is graphed"
A student page of four intercept-form equations — f(x) = (x + 2)(x + 6), f(x) = −(x − 2)(x + 8), f(x) = (x + 3)(x + 5), f(x) = 2(x − 3)(x − 1) — headed "Complete the following characteristics for each function that is given as an equation. Show any necessary scratch work on a separate sheet of paper."
The same nine prompts on every problem: Domain, Range, X-Intercept(s) with two answer lines, Y-Intercept, Increasing Int., Decreasing Int., two "As x → ___ , f(x) → ___" lines, and Vertex
A KEY page for the graphed problems, giving answers such as Domain (−∞, ∞), Range [−4, ∞), X-Intercepts (−3, 0) and (1, 0), Y-Intercept (0, −3), Vertex (−1, −4)
A KEY page for the equation problems, giving answers such as Range (−∞, 25], Y-Intercept (0, 16) and Vertex (−3, 25) for f(x) = −(x − 2)(x + 8)
A Name, Date and Period header on the student pages and the footer "Version 3: Intercept Form" on all four

Resource types: Worksheets & Printables, Worksheets

In the classroom

Teaching tips & learning objectives

Learning objectives

Read domain, range, intercepts and vertex directly from the graph of a parabola
Find the same characteristics from an equation written in intercept form, using the factors to locate the x-intercepts and the midpoint between them to locate the vertex
Write intervals of increase and decrease in interval notation, split at the vertex
State end behaviour on both sides as "As x → ∞, f(x) → ..." and "As x → −∞, f(x) → ...", and connect the direction to the sign of the leading coefficient
Evaluate a factored quadratic at zero to obtain the y-intercept, as in f(0) = (2)(6) = 12

Teaching tips

The two pages are a deliberate pair: page 1 reads characteristics off a picture, page 2 derives the same nine from symbols, so setting page 1 first gives students the vocabulary before the algebra
Problem 6, f(x) = −(x − 2)(x + 8), is the only one with a negative leading coefficient, which flips the range, the end behaviour and the order of the increasing and decreasing intervals — a good problem to work together
Answers are written in interval notation throughout, including square brackets on a closed endpoint such as [−4, ∞), so the convention is worth settling before the sheet is handed out
The footer reads "Version 3: Intercept Form", so the same nine-part layout exists for other quadratic forms and the pages can be swapped in as a re-test without reteaching the format
Before using the marking page, check problem 7: its increasing and decreasing intervals are given as (−3, ∞) and (−∞, −3), while its own vertex entry of (−4, −1) puts the turning point at x = −4

Skills covered

Reading a parabola's features from its graph — the first four problems ask for domain, range, both intercepts and the vertex from a picture alone.
Working from intercept form — the factored equations give the x-intercepts directly, as in f(x) = 2(x − 3)(x − 1) crossing at (1, 0) and (3, 0).
Locating a vertex by symmetry — the turning point sits midway between the two roots, so f(x) = (x + 2)(x + 6) has its vertex at x = −4 and value −4.
Interval notation — every answer is written as an interval or an ordered pair, from Domain (−∞, ∞) to Range (−∞, 9] and Increasing Int. (2, ∞).
End behaviour — both directions are recorded for each function, and the negative-leading-coefficient problem sends both arms to −∞ rather than ∞.

Good to know

Questions teachers ask about this resource

How do the two student pages differ?

By what students start from. The first gives four parabolas as graphs and asks for the nine characteristics to be read off; the second gives four equations already in factored intercept form and asks for the same nine to be derived, with scratch work on a separate sheet.

Which notation do the answers use?

Interval notation for domains, ranges and intervals of increase or decrease, and ordered pairs for intercepts and vertices. The marking pages show Domain (−∞, ∞), Range [−4, ∞) with a square bracket at the closed endpoint, Increasing Int. (−1, ∞) and Vertex (−1, −4).

What does "Version 3: Intercept Form" in the footer mean?

That this sheet is one form of a repeated layout. The same nine-characteristic template is numbered as a version and labelled by the algebraic form it uses, so a class can meet the identical task written for a different quadratic form without learning a new page.