Sketching Quadratic Graph Worksheets

Printable “Quadratic Equations” worksheets:
Solve Quadratic Equation (use factoring)
Solve Word Problems using Quadratic Equations
Sketching Quadratic Graphs

Rewrite Expressions in Completed-Squared Form
Solve Quadratic Equation (use completing the square)
Solve Quadratic Equation (use quadratic formula)
Discriminant in the Quadratic Formula

Examples, solutions, videos, and worksheets to help Algebra 1 students learn how to sketch quadratic graphs by identifying key features of the graph: x-intercepts, y-intercept, line of symmetry, vertex, opens upwards or downwards.

How to sketch quadratic graphs?

To sketch the graph of a quadratic equation, we’ll go through some essential steps. Here’s how to graph a quadratic function in the general form:

1. Understanding the Quadratic Equation Form
   The general form of a quadratic equation is:
   𝑦 = 𝑎𝑥² + 𝑏𝑥 + 𝑐
   where:
   𝑎 determines the direction (upward if 𝑎 > 0 and downward if 𝑎 < 0).
   𝑏 affects the position and shape of the graph.
   𝑐 is the y-intercept, which shows where the graph crosses the y-axis.
   
2. Find the Vertex
   The vertex (or turning point) of a quadratic graph is either the minimum or maximum point:
   The x-coordinate of the vertex is given by:
   𝑥 = −𝑏/(2𝑎)
   Substitute this x-value into the equation to find the corresponding y-coordinate of the vertex.
   
3. Find the Y-Intercept
   Set 𝑥 = 0 to find the y-intercept, 𝑦 = 𝑐.
   
4. Find the X-Intercepts (if they exist)
   Set 𝑦 = 0 and solve for 𝑥 to find the x-intercepts.
   Use factoring, completing the square, or the quadratic formula.
   If the discriminant 𝑏² − 4𝑎𝑐 is positive, there are two x-intercepts; if it’s zero, there’s one (the vertex lies on the x-axis), and if it’s negative, there are no x-intercepts.
   
5. Plot Points and Sketch the Graph
   Plot the vertex, y-intercept, and x-intercepts.
   Choose additional x-values around the vertex and calculate their corresponding y-values to get a few more points.
   Draw a smooth curve through these points to form a “U”-shaped parabola (upward if 𝑎 > 0 and downward if 𝑎 < 0).

Have a look at this video if you need to review how to Sketch Quadratic Graphs.

• Sketching Quadratics

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More Sketching Quadratic Graph Worksheets

Printable
(Answers on the second page.)
Sketching Quadratic Graph Worksheet #1
Sketching Quadratic Graph Worksheet #2
Sketching Quadratic Graph Worksheet #3
Sketching Quadratic Graph Worksheet #4
Sketching Quadratic Graph Worksheet #5

Online or Generated
Factor Binomials by Difference of Squares
Factor Perfect Square Trinomials

Factor Trinomials or Quadratic Equations
Factor Different Types of Trinomials 1
Factor Different Types of Trinomials 2

Solve Trinomials using Quadratic Formula
Find Discriminants of Quadratic Polynomials

Related Lessons & Worksheets

Sketching Quadratic Graphs
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Multi-step Word Problems (using +, -, ×)

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