Quadratic graph
Graph y=x^2-4x+3
Method: Use factoring and completing the square to predict key points.
- 1Factor to find x-intercepts 1 and 3.
- 2Rewrite as (x-2)^2-1 for vertex (2,-1).
- 3Plot an upward-opening symmetric parabola.
Final answer
Free online calculator
Graphing Calculator
Plot a function, inspect its curve, and explore important features on an interactive graph.
Step-by-step solutions
Clear, detailed explanations
Instant results
Accurate answers in seconds
Free to use
No sign-up required
How to Use the Graphing Calculator
1
Enter a function
Type a function such as y = x^2 - 4x + 3.
2
Create the graph
Ask the calculator to graph or plot the expression.
3
Explore the curve
Inspect the interactive graph and the accompanying analysis.
Example
How the Graphing Calculator Chooses a Method
Plot a function and connect its formula with intercepts, domain, transformations, and end behavior.
The calculator samples valid points across the viewing window and plots the resulting curve. A reliable interpretation also checks domain restrictions, intercepts, discontinuities, and whether the chosen window hides important behavior.
Supported problem types
- Polynomial, rational, trigonometric, exponential, and logarithmic graphs
- Adjustable real-variable viewing windows
- Visual inspection of roots, turning points, and discontinuities
Limits and assumptions
- A finite plot window cannot prove global behavior.
- Near asymptotes, connected sample points can look misleading unless domain breaks are considered.
Worked Graphing Calculator Examples
Each example names the method, shows the ordered reasoning, and keeps the final answer separate so you can check your own work.
Reciprocal graph
Graph y=1/x
Method: Identify domain and asymptotes before plotting.
- 1x=0 is excluded from the domain.
- 2Both axes are asymptotes.
- 3Plot branches in quadrants I and III.
Final answer
Sine transformation
Graph y=2 sin(x)
Method: Scale the parent sine graph vertically.
- 1The period remains 2pi.
- 2The amplitude changes from 1 to 2.
- 3Zeros remain at integer multiples of pi.
Final answer
Learn This Topic
What the Graphing Calculator Helps You Understand
Plot a function, inspect its curve, and explore important features on an interactive graph.
Learning focus 1
Type a function such as y = x^2 - 4x + 3.
Learning focus 2
Ask the calculator to graph or plot the expression.
Learning focus 3
Inspect the interactive graph and the accompanying analysis.
Input tips
- • Type a function such as y = x^2 - 4x + 3.
- • You can graph common polynomial, trigonometric, exponential, logarithmic, and rational functions.
Common mistakes to avoid
- • Ignoring domain restrictions and discontinuities.
- • Using a viewing window that hides intercepts or end behavior.
Frequently Asked Questions
What kinds of functions can I graph?
You can graph common polynomial, trigonometric, exponential, logarithmic, and rational functions.
Can I interact with the graph?
Yes. You can zoom, pan, and inspect the plotted curve.
Why can a graphing window be misleading?
A narrow window may hide intercepts, turning points, or end behavior; inspect the formula and adjust the range.
Does a graph prove the exact roots?
No. A graph estimates their location; use an equation solver for exact or verified numerical roots.