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Understanding Quadratic Equations

Learn about quadratic equations, their components, and their graphical representation. Explore the concepts of discriminant, complex numbers, parabolas, and quadratic functions.

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Understanding Quadratic Equations

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  1. Introductory AlgebraGlossary Chapter Ten

  2. quadratic equation • A quadratic equation is anequation that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers,with a 0.

  3. discriminant • The quantity under the radical in the quadratic formula, b2 - 4ac.

  4. complex number • Any number that can be written in the form a + bi, where a and b are real numbers.

  5. imaginary number • A complex number a + bi • with b  0.

  6. real part • The real part of a complex • number a + bi is a.

  7. imaginary part • The imaginary part of the • complex number a + bi is b.

  8. standard form of a complex number • The standard form of a • complex number is a + bi.

  9. conjugate of a complex number • The conjugate of a complex • number a + bi is a - bi.

  10. parabola • The graph of a second-degree (quadratic) equation in two variables is called a parabola.

  11. parabola • The graph of a second-degree (quadratic) equation in two variables is called a parabola.

  12. axis (axis of symmetry) • The axis of a parabola is thevertical or horizontal line through the vertex of the parabola.

  13. quadratic function • A function defined by an equation of the form f(x) = ax2 + bx + c, for real numbers a, b, and c, with a 0.

  14. Return toIntroductory Algebra • Created by • James Q. Jacobs • Superstition Mountain Campus • Central Arizona College

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