Sketching Quadratic Graph Worksheets

Printable “Quadratic Equations” worksheets:
Solve Quadratic Equation (use factoring)
Solve Quadratic Equation (use quadratic formula)
Solve Word Problems using Quadratic Equations
Sketching Quadratic Graphs
Completing the Square

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
Word Problems (Multiplication & Division)
2-Step Word Problems (Multiply/Divide/Add/Subtract)
Multi-step Word Problems (using +, -, ×)

More Printable Worksheets

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