Sketching Quadratic Graph Worksheets


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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 = π‘Žπ‘₯2 + 𝑏π‘₯ + 𝑐
    where:
    π‘Ž determines the direction (upward if π‘Ž > 0 and downward if π‘Ž < 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:
    π‘₯ = βˆ’π‘/(2π‘Ž)
    Substitute this x-value into the equation to find the corresponding y-coordinate of the vertex.
  3. Find the Y-Intercept
    Set π‘₯ = 0 to find the y-intercept, 𝑦 = 𝑐.
  4. Find the X-Intercepts (if they exist)
    Set 𝑦 = 0 and solve for π‘₯ to find the x-intercepts.
    Use factoring, completing the square, or the quadratic formula.
    If the discriminant 𝑏2 βˆ’ 4π‘Žπ‘ 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 π‘Ž > 0 and downward if π‘Ž < 0).


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

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Sketching Quadratic Graph Worksheets.

Sketching Quadratic Graph
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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

Sketching Quadratic Graphs
Word Problems (Multiplication & Division)
2-Step Word Problems (Multiply/Divide/Add/Subtract)
Multi-step Word Problems (using +, -, Γ—)

More Printable Worksheets




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