Algebra 1 Graphing Quadratic Functions and Transformations Worksheet (PDF)

Algebra 1 math worksheet: Graphing Quadratic Functions and Transformations – Maths PDF

This quadratic functions worksheet for Algebra 1 covers graphing quadratic functions and transformations (Common Core F-IF.C.7a, F-IF.C.8a, F-BF.B.3, A-SSE.B.3b), with a free PDF to print.

Quadratic functions worksheet (Algebra 1) – first page of the printable PDF
This worksheet has 20 problems on graphing quadratic functions and transformations, aligned to Common Core F-IF.C.7a, F-IF.C.8a, F-BF.B.3, and A-SSE.B.3b. You will find the vertex, axis, and intercepts of parabolas, write vertex form, describe transformations, and solve maximum and minimum problems. Early problems check one skill at a time; the final six put the skill inside real situations. Write each step on paper before you look at the answer key.

Algebra 1 · Common Core State Standards: F-IF.C.7a, F-IF.C.8a, F-BF.B.3, A-SSE.B.3b

Quadratic functions worksheet: exercises 1 to 10

Exercise 1 – Read vertex form

Identify the vertex, the axis of symmetry, and the direction of opening of \(y = (x – 2)^{2} + 3\).

Exercise 2 – Negative leading coefficient

Identify the vertex, axis, direction, and the maximum or minimum value of \(y = -2(x + 1)^{2} + 5\).

Exercise 3 – Graph a quadratic

Graph \(y = x^{2} – 4x + 3\). Label the vertex, intercepts, and axis of symmetry.

Exercise 4 – Vertex from standard form

Find the axis of symmetry and the vertex of \(y = x^{2} + 6x + 5\).

Exercise 5 – Zeros and vertex

xy-2-1123456-3-2-1123456(0, 0)(4, 0)(2, 4)
A downward-opening parabola.

Find the zeros and the vertex of \(y = -x^{2} + 4x\).

Exercise 6 – Intercepts

Find the y-intercept and the x-intercepts of \(y = x^{2} – 2x – 8\).

Exercise 7 – Shift up

Describe how the graph of \(y = x^{2} + 3\) is related to the graph of \(y = x^{2}\).

Exercise 8 – Shift right

Describe how the graph of \(y = (x – 4)^{2}\) is related to \(y = x^{2}\).

Exercise 9 – Stretch and reflect

Describe how the graphs of \(y = -x^{2}\), \(y = 3x^{2}\), and \(y = \frac{1}{2}x^{2}\) compare with \(y = x^{2}\).

Exercise 10 – Write a transformation

Write the equation of the parabola obtained by shifting \(y = x^{2}\) left 2 units and down 5 units.

Exercises 11 and up

Exercise 11 – Complete the square

Write \(y = x^{2} + 6x + 5\) in vertex form.

Exercise 12 – Vertex form with a harder constant

Write \(y = x^{2} – 8x + 10\) in vertex form and state the vertex.

Exercise 13 – Compare minimum values

Function \(f(x) = (x – 3)^{2} + 2\) and function \(g(x) = x^{2} + 4x + 1\). Which has the greater minimum value?

Exercise 14 – Domain and range

State the domain and range of \(y = -x^{2} + 6x – 5\).

Exercise 15 – Symmetric points

For \(f(x) = x^{2} – 6x + 8\), find \(f(1)\) and \(f(5)\). What do the results suggest about the axis of symmetry?

Exercise 16 – Ball height

xy123410203040506070(2, 69)
Height of a ball in feet.

A ball’s height in feet after \(t\) seconds is \(h = -16t^{2} + 64t + 5\). Find the time of the maximum height and the maximum height.

Exercise 17 – Maximum revenue

xy246810121416182022-100100200300400500600(10, 500)
Revenue in dollars at price p.

A shop’s revenue is \(R = -5p^{2} + 100p\) dollars when the price is \(p\) dollars. Find the price that gives the maximum revenue and the maximum revenue.

Exercise 18 – Fence for a pen

x20 – x
A pen with perimeter 40 feet.

A farmer has 40 feet of fence for a rectangular pen. If one side is \(x\) feet, the other side is \(20 – x\) feet, so the area is \(A = x(20 – x)\). Find the side that gives the greatest area and that area.

Exercise 19 – Arch

xy-112345678910111213-112345(0, 0)(6, 4)(12, 0)
The arch.

An arch is modeled by \(y = -\frac{1}{9}(x – 6)^{2} + 4\) (feet). Find the greatest height and where the arch meets the ground.

Exercise 20 – Maximum profit

Items x11121314Profit P208212212208
Profit near the vertex.

A store’s profit is \(P = -2x^{2} + 50x – 100\) dollars for \(x\) items. The vertex is at \(x = 12.5\). For whole numbers of items, find the maximum profit.

Exercise 21 – Describe all the changes

Describe how \(g(x) = -2(x – 1)^{2} + 3\) is obtained from \(f(x) = x^{2}\), and give its vertex.

View solution

Key facts behind this quadratic functions worksheet

Key facts
  • Standard form f(x) = ax² + bx + c; vertex form f(x) = a(x – h)² + k.
  • The axis of symmetry is x = -b/(2a), and the vertex lies on it.
  • If a > 0 the parabola opens up (minimum); if a < 0 it opens down (maximum).
  • f(x) + k shifts up/down; f(x – h) shifts right/left; a·f(x) stretches or reflects.
  • The vertex gives the maximum or minimum value in a model.

How to use this quadratic functions worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the quadratic functions worksheet as a PDF with the button below and keep it with your notes.

Download the quadratic functions worksheet as a PDF with the button below and keep it with your notes.

Related pages

All Algebra 1 chapters: Algebra 1 math.

Voter.. post

Print this page

Download PDFDownload the Algebra 1 Graphing Quadratic Functions and Transformations Worksheet (PDF, 87 KB)

More Algebra 1 math

Lessons

See all

Worksheets

See all

Tests

See all

Quizzes

See all