![]() ![]() When there are no intersection points of the graph with the x-axis, we get not real solutions (or 2 complex solutions). When there is 1 intersection point of the graph with the x-axis, there is 1 solution to the quadratic equation. When there are 2 intersection points of the graph with the x-axis, there are 2 solutions to the quadratic equation. Sometimes, we will need to do some algebra to get the. The solutions to the quadratic equation are the roots of the quadratic function, that are the intersection points of the quadratic function graph with the x-axis, when Remember, to use the Quadratic Formula, the equation must be written in standard form, ax2 + bx + c 0. The quadratic function is a second order polynomial function: When Δ=0, there is one root x 1=x 2=-b/(2a). The quadratic formula can be used to solve any quadratic equation but is best saved for when an equation cannot be factorised. The Quadratic Formula, xbb24ac2a x b b 2 4 a c 2 a, is found by completing the square of the quadratic equation.This expression is important because it can tell us about the solution: The quadratic formula with discriminant notation: The expression inside the square root is called discriminant and is denoted by Δ: The solution to the quadratic equation is given by the quadratic formula: ![]() ( x - x 1)( x - x 2) = 0 Quadratic Formula We can change the quadratic equation to the form of: The solution to the quadratic equation is given by 2 numbers x 1 and x 2. Quadratic equation is a second order polynomial with 3 coefficients - a, b, c. ![]()
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