Quadratic Functions Worksheet – Vertex Form Practice

About this resource

What's inside this resource

Quadratic Functions - Vertex Form Worksheet gives students practice identifying key characteristics of quadratic functions written in vertex form. Students examine eight vertex form graphs and determine the vertex, axis of symmetry, domain, range, and zeros for each. This two-page high school printables/worksheets/worksheets-by-subject/math-worksheets">math worksheet can be utilized in multiple ways - teachers can assign it to individual students, small groups, or the entire class to reinforce their understanding of graphing quadratic functions. By completing these real-world problems, students gain experience extracting vital information from the vertex form of quadratics, a skill that will serve them in future algebra and precalculus courses. This useful resource develops math literacy aligned to high school algebra standards.

In the classroom

Teaching tips & learning objectives

Learning objectives

State the domain and range of a quadratic function in interval notation, using a closed bracket at the vertex value and an open bracket at infinity
Read x-intercepts, the y-intercept and the vertex from a parabola's graph and write each as an ordered pair
Identify the increasing and decreasing intervals of a parabola and express them as intervals split at the axis of symmetry
Describe end behaviour with the paired statements "As x → ∞, f(x) → …" and "As x → −∞, f(x) → …", distinguishing an upward from a downward parabola
Extract the same nine characteristics from a vertex-form equation without a graph supplied, for example finding that f(x) = (x−6)²−4 has x-intercepts (4, 0) and (8, 0)

Teaching tips

Page 1 and page 2 test the same nine characteristics from opposite starting points, so working page 1 first gives students the graphical picture they then have to reconstruct mentally on page 2
The vertex is the pivot for four of the nine blanks — range, increasing interval, decreasing interval and vertex itself — so establishing it before anything else shortens each problem considerably
Two of the four equations open downward (−3(x+2)² and −(x+3)²+9) and two open upward, which makes the set usable as a sorting task on the sign of a before any calculation begins
Only problem 5 has a single x-intercept, since its vertex sits on the axis; it is the natural discussion point for how many roots a parabola can have
The direction line asks for scratch work on a separate sheet, so pair page 2 with lined paper rather than expecting the working to fit in the blanks

Skills covered

Reading key features from a parabola — students take domain, range, both intercepts and the vertex directly off four graphed quadratics on page 1.
Writing intervals in interval notation — solutions such as Range (−∞, 4], Range [−9, ∞) and Increasing Int. (−∞, 2) require the correct choice between round and square brackets.
Describing end behaviour — each problem carries the paired prompts "As x → ______, f(x) → ______", so students state the limit in both directions and match it to the parabola's orientation.
Interpreting vertex form algebraically — problems 5-8 hand over f(x) = 2(x−3)²−2 and similar with no graph, so the vertex, direction of opening and intercepts have to come from the equation itself.
Finding intercepts by substitution and solving — the y-intercept of f(x) = (x−6)²−4 is (0, 32) and its x-intercepts are (4, 0) and (8, 0), both of which require working rather than reading.

Good to know

Questions teachers ask about this resource

How are the eight problems presented to students?

In two halves. Problems 1-4 supply a graph and ask for its characteristics; problems 5-8 supply only the equation in vertex form, such as f(x) = 2(x−3)²−2, under the direction "Show any necessary scratch work on a separate sheet of paper".

What has to be filled in for each function?

Nine entries every time: domain, range, x-intercept(s), y-intercept, increasing interval, decreasing interval, two end-behaviour limits and the vertex. The layout is identical for all eight problems.

Which notation do the worked solutions use?

Interval notation with the bracket distinction observed — Domain (−∞, ∞), Range (−∞, 4] for a downward parabola and [−9, ∞) for an upward one — while intercepts and vertices are written as ordered pairs such as (−4, 2) and (0, −9).