![]() Factoring - The process of breaking apart of an equation into factors (or. We can do the same to expand an expression with a sum and a difference, such as \((x 5)(x-2)\), or to expand an expression with two differences, for example, \((x-4)(x-1)\). Quadratic Equation - An equation that can be written in the form ax2 bx c 0. This equation arose from finding the time when a. In a previous lesson we saw how to use a diagram and to apply the distributive property to multiply two linear expressions, such as \((x 3)(x 2)\). (b) 5 3t 4.9t2 0 is a quadratic equation in quadratic form. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations. When the quadratic expression is a product of two factors where each one is a linear expression, this is called the factored form.Īn expression in factored form can be rewritten in standard form by expanding it, which means multiplying out the factors. ![]() The function \(f\) can also be defined by the equivalent expression \((x 2)(x 1)\). The standard form is ax bx c 0 with a, b and c being constants, or numerical coefficients, and x being an unknown variable. Notice that its completed square form is exactly the same as its factored form. We refer to \(a\) as the coefficient of the squared term \(x^2\), \(b\) as the coefficient of the linear term \(x\), and \(c\) as the constant term. graphing factoring completing the square using the quadratic formula. In general, standard form is \(\displaystyle ax^2 bx c\) The quadratic expression \(x^2 3x 2\) is called the standard form, the sum of a multiple of \(x^2\) and a linear expression ( \(3x 2\) in this case). For example, a quadratic function \(f\) might be defined by \(f(x) = x^2 3x 2\). ![]() ![]() A quadratic function can often be represented by many equivalent expressions. ![]()
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