![]() Converting a quadratic function from standard form to factored FormĬonvert \(f(x)=2x^2+7x+3\) into factored form. In order to efficiently find the zeros, we must first convert the equation to factored form. ![]() ![]() It is useful to be able to convert the same quadratic function equation to different forms.įor instance, you may be asked to find the zeros, or x-intercepts, of a quadratic function equation given in the standard form. Converting between different forms of quadratic functionsĭifferent scenarios may require you to solve for different key features of a parabola. Notice, that the axis of symmetry is located at the x-value of the vertex. Therefore, the equation of the axis of symmetry for this quadratic function is \(x=2\). This vertex is located on the axis of symmetry of the parabola. Recall that the vertex form of a quadratic equation isīy comparison, \(h\) is \(2\), while \(k\) is \(-1\). Standard form (general form) of a quadratic function Understanding the benefits of each form of a quadratic function will be useful for analyzing different situations that come your way. Factored or Intercept Form: \(y=a(bx+c)(dx+e)\)Įach of these forms can be used to determine different information about the path of a projectile.Standard or General Form: \(y=ax^2+bx+c\).There are three commonly used forms of quadratic functions. What are the forms of quadratic functions? In this explanation, we will explore the various forms of Quadratic functions, and see how to convert them from one to the other. In these scenarios, you can use Quadratic functions to learn how high the object will travel and where it will land. Have you ever launched a toy rocket? The path of a rocket being launched into the air and falling back to the ground can be modeled by the graph of a quadratic function.Īrched paths are found for other activities involving projectiles, including shooting a cannonball and hitting a golf ball.
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