Worksheets · Algebra 1

Graphing quadratic functions worksheet

A grid comes with every question and the answer key has the curve drawn on it. Vertex form shows the turning point, factored form shows where it crosses the x-axis, and standard form needs the vertex worked out. Some questions give the graph and ask for the solutions of the equation.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Quadratic Functions

Date Period

Graph each function, or use the graph as asked.

  1. Graph a quadratic in vertex form

    Graph y=−(x+3)2−10−10−5−5551010
  2. Graph y=(x+1)2+2−10−10−5−5551010
  3. Graph y=(x−2)2−3−10−10−5−5551010
  4. Graph y=−(x−3)2+2−10−10−5−5551010
  5. Graph y=−(x+1)2+3−10−10−5−5551010

  1. Graph a quadratic in standard form

    Graph y=−x2+6x−11−10−10−5−5551010
  2. Graph y=x2+4x−10−10−5−5551010
  3. Graph y=x2−4x+5−10−10−5−5551010
  4. Graph y=−x2+4x−10−10−5−5551010
  5. Graph y=x2+2x−2−10−10−5−5551010

  1. Graph a quadratic in factored form

    Graph y=x(x−4)−10−10−5−5551010
  2. Graph y=(x−1)(x−3)−10−10−5−5551010
  3. Graph y=(x+4)(x+2)−10−10−5−5551010
  4. Graph y=(x+2)(x−2)−10−10−5−5551010
  5. Graph y=(x+3)(x−1)−10−10−5−5551010

  1. Solve using the graph

    The graph of y=x2+5x is shown. Use it to solve x2+5x=0−10−10551010−5
  2. The graph of y=x2−9x+18 is shown. Use it to solve x2−9x+18=0−10−10−5−5551010
  3. The graph of y=x2−9 is shown. Use it to solve x2−9=0−10−10−5−5551010
  4. The graph of y=x2+6x+5 is shown. Use it to solve x2+6x+5=0−10−10−5551010
  5. The graph of y=x2+x−6 is shown. Use it to solve x2+x−6=0−10−10−5551010−5

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Quadratic FunctionsAnswer keyVersion 1

Date Period

Graph each function, or use the graph as asked.

  1. Graph a quadratic in vertex form

    Graph y=−(x+3)2−10−10−5551010−5vertex (−3,0), opens down
  2. Graph y=(x+1)2+2−10−10−5−5551010vertex (−1,2), opens up
  3. Graph y=(x−2)2−3−10−10−5−5510105vertex (2,−3), opens up
  4. Graph y=−(x−3)2+2−10−5−551010−105vertex (3,2), opens down
  5. Graph y=−(x+1)2+3−10−10−5−5551010vertex (−1,3), opens down

  1. Graph a quadratic in standard form

    Graph y=−x2+6x−11−10−10−5−5551010Vertex (3,−2), opens down
  2. Graph y=x2+4x−10−10−5−5551010Vertex (−2,−4), opens up
  3. Graph y=x2−4x+5−10−10−5−5551010Vertex (2,1), opens up
  4. Graph y=−x2+4x−10−5551010−10−5Vertex (2,4), opens down
  5. Graph y=x2+2x−2−10−10−5−5551010Vertex (−1,−3), opens up

  1. Graph a quadratic in factored form

    Graph y=x(x−4)−10−10−5−5510105Roots 0 and 4, vertex (2,−4)
  2. Graph y=(x−1)(x−3)−10−10−5−5510510Roots 1 and 3, vertex (2,−1)
  3. Graph y=(x+4)(x+2)−10−10−5−5510105Roots −4 and −2, vertex (−3,−1)
  4. Graph y=(x+2)(x−2)−10−10−5−5551010Roots −2 and 2, vertex (0,−4)
  5. Graph y=(x+3)(x−1)−10−10−5−5551010Roots −3 and 1, vertex (−1,−4)

  1. Solve using the graph

    The graph of y=x2+5x is shown. Use it to solve x2+5x=0−10−10551010−5{−5,0}
  2. The graph of y=x2−9x+18 is shown. Use it to solve x2−9x+18=0−10−10−5−5551010{3,6}
  3. The graph of y=x2−9 is shown. Use it to solve x2−9=0−10−10−5−5551010{−3,3}
  4. The graph of y=x2+6x+5 is shown. Use it to solve x2+6x+5=0−10−10−5551010{−5,−1}
  5. The graph of y=x2+x−6 is shown. Use it to solve x2+x−6=0−10−10−5551010−5{−3,2}

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Graph y=(x−2)2−3

  1. The vertex is at (2, -3).
  2. The coefficient is positive, so it opens up.
  3. Plot a point either side and mirror them.

The answer is vertex (2,−3), opens up.

Where students go wrong

Reading the vertex with the wrong sign. (x - 2)² has its vertex at x = 2, not -2, because that is the value making the parenthesis zero. The other slip is plotting only one side and forgetting a parabola is symmetric.

Also called vertex form graphs or plotting quadratics.

What you can put on this worksheet

Vertex form
Graph y=−x2+2 → vertex (0,2), opens down
Standard form
Graph y=−x2+2 → Vertex (0,2), opens down
Factored form
Graph y=x(x+4) → Roots −4 and 0, vertex (−2,−4)
Solve from the graph
The graph of y=x2−1 is shown. Use it to solve x2−1=0 → {−1,1}

Questions about these worksheets

Yes. Every graphing quadratic functions sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the graphing quadratic functions questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 4: vertex form, standard form, factored form and solve from the graph. Tick as many as you want and set how many of each, or let it spread them evenly.

Reading the vertex with the wrong sign. (x - 2)² has its vertex at x = 2, not -2, because that is the value making the parenthesis zero. The other slip is plotting only one side and forgetting a parabola is symmetric.