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The solutions of the quadratic equation + + = may be deduced from the graph of the quadratic function = + +, which is a parabola. If the parabola intersects the x -axis in two points, there are two real roots , which are the x -coordinates of these two points (also called x -intercept).
The graph of a real single-variable quadratic function is a parabola. If a quadratic function is equated with zero, then the result is a quadratic equation . The solutions of a quadratic equation are the zeros (or roots ) of the corresponding quadratic function, of which there can be two, one, or zero.
In the theory of quadratic forms, the parabola is the graph of the quadratic form x 2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x 2 + y 2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x 2 − y 2. Generalizations to more variables yield ...
The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola , the parabola , and the ellipse ; the circle is a special case of the ellipse, though it was sometimes considered a fourth type.
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
The logistic map is a discrete dynamical system defined by the quadratic ... The graph has the shape of a parabola, and the vertex of the parabola changes as the ...
Given a quadratic polynomial of the form + the numbers h and k may be interpreted as the Cartesian coordinates of the vertex (or stationary point) of the parabola. That is, h is the x -coordinate of the axis of symmetry (i.e. the axis of symmetry has equation x = h ), and k is the minimum value (or maximum value, if a < 0) of the quadratic ...