Probably the easiest type of quadratic equation to solve is one where \(b = 0\) i.e. ![]() This page outlines three different techniques. There are various ways of solving quadratic equations, depending on the nature of the equation. The second image is an example of where the parabola intersects the \(x\) axis twice, and hence there are two solutions, and finally the third image is an example of where the parabola does not intersect the \(x\) axis at all - and hence there are no solutions. The first image below is an example of where the parabola only intersects the \(x\) axis once, and hence there is only one solution (this is actually a plot of \(y = x^2\), although no scales are included on the axes). As seen below these take the form of parabolas, and the places at which these parabolas intersect the \(x\) (horizontal) axis are the solutions to the equation (as this is when the equation is equal to \(0\)). To understand why this is the case, it can be helpful to look at the graphs of some quadratic equations. ![]() While this quadratic equation has only one solution, note that often there will be two solutions, and sometimes there will be no (real) solutions at all. So the solution to this quadratic equation is \(0\). In this case you should be able to see that the value of the variable \(x\) must be \(0\), as only \(0^2 = 0\). The most basic quadratic equation occurs when \(a = 1\), \(b = 0\) and \(c = 0\), in which case we have: These are referred to as coefficients of the equation. Where \(x\) is a variable and \(a\), \(b\) and \(c\) represent known numbers such that \(a \neq 0\) (if \(a = 0\) then the equation is linear). In particular, the page covers the following (use the drop-down menu above to jump to a different section as required):Ī quadratic equation, or second degree equation, is an algebraic equation of the form: Now, graph the quadratic function \(y= 3x^2 – 11x + 5\) manually or using a graphing calculator and determine the \(x\)-intercepts.This page explains some techniques for solving quadratic equations. Solution: First, convert the given equation into the standard form, \(3x^2-11x+5=0\). Solve the following quadratic equation using graphing. Solving a Quadratic Equation by Graphing – Example 1: Then the \(x\)-intercept(s) of the graph (the points) that intersect the \(x\)-axis of the graph) are nothing but the roots of the quadratic equation. To solve quadratics by graphing, we must first graph the quadratic expression (when the equation is in standard form) by hand or using a graphing calculator. Solving quadratic equations by quadratic formula.Solving quadratic equations by graphing.Solving quadratic equations by completing the square.Solving quadratic equations by factoring.There are different ways of solving quadratic equations: Since the degree of a quadratic equation is \(2\), it can have at most \(2\) roots. The values that satisfy the quadratic equation are known as the root (or) solution (or) zero. Solving quadratic equations means finding the variable’s value (or values) that satisfies the equation. How to Solve a Quadratic Equation by Factoring?Ī step-by-step guide to solving a quadratic equation by graphing.How to Solve a Quadratic Equation by Completing the Square?. ![]() + Ratio, Proportion & Percentages Puzzles.
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