Live math canvas
Quadratic Formula Calculator: x = 2 or 1. Discriminant 1; roots = (-b ± √discriminant) ÷ 2a. Vertex (1.5, -0.25).
Formula applied
CalculationTime keeps the method visible so the number can be checked instead of blindly trusted.
x = (-b ± √(b² - 4ac)) ÷ 2a. Discriminant D = b² - 4ac. Vertex x-coordinate = -b ÷ 2a.Your live breakdown
These values come from the controls above and update when the calculator changes.
Resulting answer
Discriminant 1; roots = (-b ± √discriminant) ÷ 2a. Vertex (1.5, -0.25).
Assumptions used
Best for homework checks, algebra worksheets and quick root verification where the discriminant and formula should stay visible.
Master’s Tip
Master’s Tip: check the discriminant first. Positive means two real roots, zero means one repeated real root, and negative means a complex pair.
Printable record
Save the inputs, result, formula, assumptions, page URL and date together so the calculation can be reviewed later.
What-if check
The discriminant decides the root type before the quadratic formula is evaluated, so the printout preserves that checkpoint.
| Check | Value | Note |
|---|---|---|
| a, b, c | 1, -3, 2 | quadratic coefficients |
| discriminant | 1 | two real roots |
| vertex x | 1.5 | -b divided by 2a |
| current output | x = 2 or 1 | formula result |
Visual proof
Discriminant 1; roots = (-b ± √discriminant) ÷ 2a. Vertex (1.5, -0.25).
x = (-b ± √(b² - 4ac)) ÷ 2a. Discriminant D = b² - 4ac. Vertex x-coordinate = -b ÷ 2a.
For x² - 3x + 2 = 0, D = (-3)² - 4(1)(2) = 1. Roots are (3 ± 1) ÷ 2, so x = 2 or x = 1.
Master’s Tip: check the discriminant first. Positive means two real roots, zero means one repeated real root, and negative means a complex pair.
Standard or basis: ordinary real/complex algebra for second-degree polynomial equations; no curriculum-specific rounding rule is claimed.
Methodology & Accuracy
CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.
x = (-b ± √(b² - 4ac)) ÷ 2a. Discriminant D = b² - 4ac. Vertex x-coordinate = -b ÷ 2a.
Standard or basis: ordinary real/complex algebra for second-degree polynomial equations; no curriculum-specific rounding rule is claimed.
Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.Master’s Tip: check the discriminant first. Positive means two real roots, zero means one repeated real root, and negative means a complex pair.
The quadratic formula is x = (-b ± √(b² - 4ac)) ÷ 2a for equations written as ax² + bx + c = 0.
The discriminant b² - 4ac tells whether the roots are two real roots, one repeated real root, or a complex pair.
Then the equation is not quadratic. This page solves the remaining linear equation when b is not zero.
Quadratic equations connect algebra, geometry and graphing. The discriminant and vertex make the answer more useful than a bare pair of roots.
Before calculating roots, the discriminant explains the shape of the answer. It prevents confusion when a calculator returns complex values.
The same coefficients also define the parabola vertex. Showing it beside the roots helps connect equation solving to graph behavior.