Knowra Quadratic formula Quadratic formula The quadratic formula gives the roots of an equation ax² + bx + c = 0 from its coefficients. Its discriminant determines whether the roots are real or complex and whether they coincide.
Completing the square : An algebraic method that rewrites a quadratic expression as a perfect square plus or minus a constant. Applying this method to ax² + bx + c = 0 derives the quadratic formula.
Polynomial : An expression formed from variables and coefficients using nonnegative integer powers and arithmetic operations. A quadratic equation is built by setting a degree-two polynomial equal to zero.
Quadratic function : A function defined by a polynomial of degree two, whose graph is a parabola. Its zeros can be calculated with the formula, locating where its graph crosses the horizontal axis.
Factoring : Rewriting an expression as a product of simpler factors. Factoring can solve some quadratic equations more quickly, but it does not always yield simple factors.
Discriminant : For a quadratic ax² + bx + c, the quantity b² − 4ac, which classifies its roots. Its sign tells whether the formula yields two real roots, one repeated root, or complex roots.
Coefficient : A numerical or symbolic factor multiplying a term in an algebraic expression. The values a, b, and c are the formula’s inputs, with a required to be nonzero.
Parabola : A plane curve formed by points equidistant from a fixed point and a fixed line. The formula finds the x-intercepts of a parabola represented by a quadratic function.
Graphical method : A method of solving equations by plotting functions and estimating their intersections or zeros. A graph estimates quadratic roots visually, whereas the formula gives exact expressions.
Quadratic equation : An equation in one variable whose highest power is two. The formula solves this broader class of equations when the leading coefficient is nonzero.
Root of a function : An input value at which a function’s output is zero. The formula returns the inputs that make the quadratic polynomial vanish.
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