Graphing Calculator
Graph a quadratic or linear function and inspect its value, vertex and x-intercepts.
Result
Function value Y: 5
The graph rescales automatically; calculated coordinates retain their numerical values.
- Function
- y = 1x² + 0x − 4
- Graph type
- Quadratic function
- Vertex
- (0, -4)
- Real x-intercepts
- -2, 2
- Discriminant
- 16
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How to use the Graphing Calculator
- Enter A, B, and C for the function y = ax² + bx + c.
- Enter an X coordinate to evaluate the function at that point.
- Inspect the live graph, vertex, discriminant, and real x-intercepts.
Graph a quadratic or linear function
The calculator graphs the polynomial:
y = ax² + bx + cWhen a is not zero, the graph is a parabola. Its vertex has x coordinate
−b/(2a), and its real x-intercepts come from the quadratic formula. The
discriminant b² − 4ac determines whether there are two, one, or no real
intercepts.
When a = 0, the same inputs describe the straight line y = bx + c.
The formulas follow OpenStax College Algebra 2e.
With your numbers
- Substitute x = 3 into y = 1x² + 0x − 4.
- Y = 5; discriminant b² − 4ac = 16.
Quick reference
The graph rescales automatically; calculated coordinates retain their numerical values.
| Example | Function value Y |
|---|---|
| Parabola with roots at minus 2 and 2 | 5 |
| Perfect-square parabola | 9 |
| Downward parabola | 5 |
| Linear function | 9 |
| No real intercepts | 5 |
| Constant function | 5 |
Common questions about the Graphing Calculator
- Can this graph a straight line?
- Yes. Set A to zero and enter B and C for y = bx + c.
- What does the discriminant tell me?
- A positive discriminant gives two real x-intercepts, zero gives one repeated intercept, and a negative value gives no real x-intercepts.
- What is the vertex?
- The vertex is the turning point of a parabola. Its x coordinate is −b divided by 2a.
- Why does the graph scale change?
- The preview automatically scales the visible y range so the entered function remains visible.