In each case the parameter a determines the vertical stretching of the graph.Ĭhoose the two roots of the parabola, and observe how the x-intercepts change to reflect each root. Converting a quadratic function to standard form is called completing the square. The vertex of the graph is located at the point h, k. Instead, we turn to a different form- the factored form of a quadratic equation is y a ( x r ) ( x s ) ya(x-r)(x-s) ya(xr)(xs). Standard form, the sum of a constant term, k and a constant, a times the square of a linear term: Converting a quadratic function to expanded form is called expanding. The -2 and the 18 are the solutions to the quadratic function, which in this case means that this will be either a real (18) or hypothetical (-2) time when the rocket is on ground level. The parameter c is the y -intercept, while the parameter b is the slope of the tangent at 0. The equation often uses t instead of x because t would stand for time and f(t) is height above ground. ![]() Įxpanded form, a sum of terms, each of which may be a product of a constant and some variables: Converting a quadratic function to factored form is called factoring. Apart from the standard form of quadratic equation, a quadratic equation can be written in other forms. ![]() This equation is called quadratic as its degree is 2 because quad means square. The parameters p and q are the roots of the function (the x -intercepts of the graph y = f x ). The standard form of quadratic equation is ax 2 + bx + c 0, where a is the leading coefficient and it is a non-zero real number. Quadratic functions f x can be written in three forms.įactored form, the product of a constant and two linear terms:
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