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In mathematics, a quadratic function of a single variable is a function of the form [1] = + +,,where is its variable, and , , and are coefficients.The expression + + , especially when treated as an object in itself rather than as a function, is a quadratic polynomial, a polynomial of degree two.
Quadratic equation graph key points: Image title: Graph of y = ax² + bx + c having real roots and positive a with key points labellled by CMG Lee. Roots and y-intercept are in red, turning point and axis of symmetry are in purple, and focus and directrix are in blue. Values are given in terms of the discriminant, b² - 4ac.
Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0). A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.
Quadratic function graph complex roots: Image title: Visualisation of the complex roots of y = ax² + bx + c where a is positive and the discriminant, b² - 4ac is negative, by CMG Lee. The parabola is rotated 180° about its vertex (yellow). Its roots are rotated 90° around their mid-point, and the plane is interpreted as the complex plane ...
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.
English: The Quadratic Formula, used to find the value of x in the equation ax 2 +bx+c=0. Date: ... Storing formulas as images makes it harder to change them. TeX ...
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 ...
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 function. One way to see this is to note that the graph of the function f ( x ) = x 2 is a parabola whose vertex is at the origin (0, 0).
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