![]() Now we can add this value as a constant within our trinomial. Now we can proceed to find the zeros, roots, or x-intercepts by setting the function equation equal to zero and applying the zero product property. Therefore, our resulting equation in factored form is \(f(x)=(2x+1)(x+3)\). Therefore, we can factor the entire expression by applying the distributive property. In this case, \(2x\) can be factored out of the first two terms and \(1\) can be factored out of the last two terms. Now we can factor out the GCF of each group. We can now split the middle term and rewrite the expression as follows: The two values whose product is \(6\) and sum up to \(7\) are \(1\) and \(6\). We can list the factors of \(6\) and their sums as follows: To do this, find the factors of the product of the values of \(a\) and \(c\) that also sum up to make \(b\). In order to factor the expression, we can factor the expression by grouping. Let’s recall what Factored Form looks like this: \(f(x)=a(x-r_1)(x-r_2)\). To convert from the standard form into factored form, we need to factor the expression \(2x^2+7x+3\). 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.
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