Resources/Interactive Function Plotter
Grades 9-10•Printable worksheet + answer key•CC0 license

Interactive Function Plotter

Explore linear and quadratic functions by dragging points on the graph.

A hands-on tool for understanding how equation parameters affect graph shape. Drag points to change slope, intercepts, and vertex position.

Print-ready worksheet with answer key and quick teaching tips.

Grades 9-100 problems10 minAnswer key included
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Ready-to-teach

Clear steps, examples, and practice in one printable page.

Misconception-proof

Highlights common mistakes and how to fix them quickly.

Open license

CC0: free to copy, adapt, and share without attribution.

Quick overview

This interactive function plotter helps students in grades 9-10 understand the connection between equations and their graphs. Explore linear functions (y = mx + b) and quadratic functions (y = ax² + bx + c) by dragging control points.

Learning targets

  • Understand how slope affects the steepness of a line.
  • Identify y-intercept and x-intercept from a graph.
  • Explore how vertex position affects a parabola's shape.
  • Connect equation parameters (m, b, a, h, k) to visual features.
  • Distinguish between lines that go up vs. down (positive/negative slope).
  • Recognize parabolas that open up vs. down.

Step-by-step approach

  1. 1Select Linear or Quadratic mode using the tabs.
  2. 2Drag the labeled control points on the graph.
  3. 3Watch the equation update in real-time below the graph.
  4. 4Observe how intercepts and key features change.
  5. 5Try to create specific equations by positioning the points.

Common mistakes

Mistake

Confusing slope and y-intercept in y = mx + b.

Try instead

Remember: m (slope) controls steepness, b controls where the line crosses the y-axis.

Mistake

Thinking all parabolas open upward.

Try instead

When a < 0, the parabola opens downward (like an upside-down U).

Mistake

Mixing up vertex form and standard form.

Try instead

Vertex form y = a(x-h)² + k directly shows the vertex at (h, k).

Mistake

Forgetting that the x-intercept is where y = 0.

Try instead

X-intercepts (roots) are the points where the graph crosses the x-axis.

Worked example

Guided
Graph the line y = 2x - 3 and identify its key features.
  1. The slope m = 2 means the line goes up 2 units for every 1 unit right.
  2. The y-intercept b = -3 means the line crosses the y-axis at (0, -3).
  3. To find the x-intercept, set y = 0: 0 = 2x - 3, so x = 1.5.
  4. The x-intercept is at (1.5, 0).
Answer: Line with slope 2, y-intercept (0, -3), x-intercept (1.5, 0)

Related resources

Linear equations

Slope, slope-intercept form, and graphing lines.

View resource

Quadratics

Factoring, quadratic formula, and graphing parabolas.

View resource

Coordinate plane

Plotting points and reading ordered pairs.

View resource

Interactive Function Plotter

Drag the points on the graph to explore how changing values affects the equation. Watch the equation update in real-time as you move points.

-16--15--14--13--12--11--10--9--8--7--6--5--4--3--2--1-123456789101112131415-16--15--14--13--12--11--10--9--8--7--6--5--4--3--2--1-123456789101112131415(-2.0, 0)y-intslope
y=x+2y = x + 2
Slope (m): 1.00
Y-intercept (b): (0, 2)
X-intercept: (-2.00, 0)
Green = run (horizontal), Orange = rise (vertical)

Teacher tips

  • THave students predict what will happen before dragging points.
  • TChallenge students to create a line with a specific slope and intercept.
  • TCompare parallel lines (same slope, different intercepts).
  • TExplore perpendicular lines (slopes that are negative reciprocals).
  • TFor quadratics, discuss how 'a' affects width and direction.

Parent tips

  • PAsk your child to explain what each draggable point controls.
  • PHave them describe the equation changes in their own words.
  • PRelate to real-world scenarios like ramps (slope) or thrown balls (parabolas).
  • PEncourage experimentation - there are no wrong answers when exploring!

Open license

You are free to copy, adapt, and share these materials. No attribution required. Released under Creative Commons CC0 1.0 (public domain).