Quadratic Equation Calculator

Terms may sit on both sides; they are collected to standard form first.
Root 1 (real part)
-0
Quadratic Equation Solver
Root 2 (real part)
-0
Root 1 (imaginary part)
0
Root 2 (imaginary part)
0
Roots
x = 0 (double root)
Discriminant b^2 - 4ac
0
Nature of the roots
one repeated real root
Vertex x (axis of symmetry)
-0
Vertex y (minimum or maximum)
0
Parabola opens
upward (vertex is the minimum)
y-intercept
0
Sum of roots (-b/a)
-0
Product of roots (c/a)
0
Standard form
x^2 = 0
Factored form
xx
Vertex form
(x - 0)^2 + 0
Worked out from OpenStax, College Algebra 2e, Section 2.5: Quadratic Equations and 1 other source.

How this is worked out

5 steps
  1. Standard form: x^2 = 0 with a = 1, b = 0, c = 0.
  2. Discriminant D = b^2 - 4ac = 0^2 - 4(1)(0) = 0.
  3. D = 0, so the parabola touches the axis once at x = 0 / 2 = 0.
  4. Vertex: x = -b/(2a) = 0, y = c - b^2/(4a) = 0.
  5. Vieta's formulas: sum of roots = -b/a = 0, product = c/a = 0.

Results are general information, not financial, tax, legal, medical or engineering advice.