Quadratic explorer
Move a, b and c and watch the roots appear and disappear exactly as the sign of the discriminant changes.
- Solving quadratics
- The discriminant
- Roots, vertex and intercepts
b² − 4ac
16.0
Real roots
2
Vertex
(1.0, -4.0)
y-intercept
-3.0
Predict
If b² − 4ac is negative, what does the graph look like?
Experiment
- 1Set a = 1, b = 0 and move c from −4 up to +4. Watch the roots meet and then disappear as the discriminant changes sign.
- 2Find a combination where b² − 4ac is exactly 0 and check the curve touches the axis once.
- 3Make a negative and confirm the parabola turns upside down and the vertex becomes a maximum.
- 4Set a = 0 and explain why the vertex readout stops being meaningful.
Explain
The y-intercept is always c, because putting x = 0 leaves y = c. That is the quickest check that you have sketched the right curve.
The sign of a decides which way up the parabola sits: positive gives a minimum, negative gives a maximum. Its size decides how steep the curve is.
The discriminant b² − 4ac is the part under the square root in the quadratic formula. Positive gives two real roots, zero gives one repeated root where the curve just touches the axis, and negative gives none — the formula would need the square root of a negative number.