Solve the quadratic equation

x

We have our a, b, and c values:

a = 1, b = 1, c = -12

Solve the quadratic equation

x

x = | -b ± √b^{2} - 4ac |

2a |

-b = -1

Δ = 1

Δ = 1 - -48

Δ = 49 <--- Discriminant

Since Δ > 0, we expect two real roots.

√Δ = 7

Numerator 1 = -1 + 7

Numerator 1 = 6

Numerator 2 = -1 - 7

Numerator 2 = -8

Denominator = 2 * 1

Denominator = 2

Solution 1 = | Numerator 1 | |

Denominator |

Solution 1 = | 6 | |

2 |

Solution 1 = 3

Solution 2 = | Numerator 2 | |

Denominator |

Solution 2 = | -8 | |

2 |

Solution 2 = -4

(9) + 312 ? 0

9 + 312 ? 0

0 = 0

(16) - 412 ? 0

16 - 412 ? 0

0 = 0

(Solution 1, Solution 2) = (3, -4)

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax^{2} + bx + c = 0. Also generates practice problems as well as hints for each problem.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)^{2} + k

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

This calculator has 4 inputs.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

This calculator has 4 inputs.

- y = ax
^{2 + bx + c} - (-b ± √b
^{2}- 4ac)/2a - h (Axis of Symmetry) = -b/2a
- The vertex of a parabola is (h,k) where y = a(x - h)
^{2 + k}

For more math formulas, check out our Formula Dossier

- complete the square
- a technique for converting a quadratic polynomial of the form ax
^{2}+ bx + c to a(x - h)^{2}+ k - equation
- a statement declaring two mathematical expressions are equal
- factor
- a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.
- intercept
- parabola
- a plane curve which is approximately U-shaped
- quadratic
- Polynomials with a maximum term degree as the second degree
- quadratic equations and inequalities
- rational root
- vertex
- Highest point or where 2 curves meet

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